
Quadratic equations
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2-15*x-(2)=0
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-15x-2
The first term is, x2 its coefficient is 1 .
The middle term is, -15x its coefficient is -15 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -15 .
-2 | + | 1 | = | -1 | |
-1 | + | 2 | = | 1 |
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 15x - 2 = 0Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-15x-2
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 7.5000
Plugging into the parabola formula 7.5000 for x we can calculate the y -coordinate :
y = 1.0 * 7.50 * 7.50 - 15.0 * 7.50 - 2.0
or y = -58.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-15x-2
Axis of Symmetry (dashed) {x}={ 7.50}
Vertex at {x,y} = { 7.50,-58.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-0.13, 0.00}
Root 2 at {x,y} = {15.13, 0.00}
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-15x-2 = 0 by Completing The Square .
Add 2 to both side of the equation :
x2-15x = 2
Now the clever bit: Take the coefficient of x , which is 15 , divide by two, giving 15/2 , and finally square it giving 225/4
Add 225/4 to both sides of the equation :
On the right hand side we have :
2 + 225/4 or, (2/1)+(225/4)
The common denominator of the two fractions is 4 Adding (8/4)+(225/4) gives 233/4
So adding to both sides we finally get :
x2-15x+(225/4) = 233/4
Adding 225/4 has completed the left hand side into a perfect square :
x2-15x+(225/4) =
(x-(15/2)) • (x-(15/2)) =
(x-(15/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-15x+(225/4) = 233/4 and
x2-15x+(225/4) = (x-(15/2))2
then, according to the law of transitivity,
(x-(15/2))2 = 233/4
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(15/2))2 is
(x-(15/2))2/2 =
(x-(15/2))1 =
x-(15/2)
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-(15/2) = √ 233/4
Add 15/2 to both sides to obtain:
x = 15/2 + √ 233/4
Since a square root has two values, one positive and the other negative
x2 - 15x - 2 = 0
has two solutions:
x = 15/2 + √ 233/4
or
x = 15/2 - √ 233/4
Note that √ 233/4 can be written as
√ 233 / √ 4 which is √ 233 / 2
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-15x-2 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -15
C = -2
Accordingly, B2 - 4AC =
225 - (-8) =
233
Applying the quadratic formula :
15 ± √ 233
x = ——————
2
√ 233 , rounded to 4 decimal digits, is 15.2643
So now we are looking at:
x = ( 15 ± 15.264 ) / 2
Two real solutions:
x =(15+√233)/2=15.132
or:
x =(15-√233)/2=-0.132
Two solutions were found :
- x =(15-√233)/2=-0.132
- x =(15+√233)/2=15.132
Similar Problems from Web Search
Share
- Day spas state college pa
- Bathroom cabinets white high gloss
- Side part curly wig
- Good feet store prices

|
Most Used Actions
\mathrm{simplify} | \mathrm{solve\:for} | \mathrm{expand} | \mathrm{factor} | \mathrm{rationalize} |

Our online expert tutors can answer this problem
Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!
In partnership with
You are being redirected to Course Hero
Correct Answer :)
Let's Try Again :(
Try to further simplify

Related
Number Line
Graph
Examples
equation-calculator
vertex y=x^{2}-15x
en
Quadratic equations
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-15x-500
The first term is, x2 its coefficient is 1 .
The middle term is, -15x its coefficient is -15 .
The last term, "the constant", is -500
Step-1 : Multiply the coefficient of the first term by the constant 1 • -500 = -500
Step-2 : Find two factors of -500 whose sum equals the coefficient of the middle term, which is -15 .
-500 | + | 1 | = | -499 | |
-250 | + | 2 | = | -248 | |
-125 | + | 4 | = | -121 | |
-100 | + | 5 | = | -95 | |
-50 | + | 10 | = | -40 | |
-25 | + | 20 | = | -5 | |
-20 | + | 25 | = | 5 | |
-10 | + | 50 | = | 40 | |
-5 | + | 100 | = | 95 | |
-4 | + | 125 | = | 121 | |
-2 | + | 250 | = | 248 | |
-1 | + | 500 | = | 499 |
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 15x - 500 = 0Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-15x-500
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 7.5000
Plugging into the parabola formula 7.5000 for x we can calculate the y -coordinate :
y = 1.0 * 7.50 * 7.50 - 15.0 * 7.50 - 500.0
or y = -556.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-15x-500
Axis of Symmetry (dashed) {x}={ 7.50}
Vertex at {x,y} = { 7.50,-556.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-16.08, 0.00}
Root 2 at {x,y} = {31.08, 0.00}
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-15x-500 = 0 by Completing The Square .
Add 500 to both side of the equation :
x2-15x = 500
Now the clever bit: Take the coefficient of x , which is 15 , divide by two, giving 15/2 , and finally square it giving 225/4
Add 225/4 to both sides of the equation :
On the right hand side we have :
500 + 225/4 or, (500/1)+(225/4)
The common denominator of the two fractions is 4 Adding (2000/4)+(225/4) gives 2225/4
So adding to both sides we finally get :
x2-15x+(225/4) = 2225/4
Adding 225/4 has completed the left hand side into a perfect square :
x2-15x+(225/4) =
(x-(15/2)) • (x-(15/2)) =
(x-(15/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-15x+(225/4) = 2225/4 and
x2-15x+(225/4) = (x-(15/2))2
then, according to the law of transitivity,
(x-(15/2))2 = 2225/4
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(15/2))2 is
(x-(15/2))2/2 =
(x-(15/2))1 =
x-(15/2)
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-(15/2) = √ 2225/4
Add 15/2 to both sides to obtain:
x = 15/2 + √ 2225/4
Since a square root has two values, one positive and the other negative
x2 - 15x - 500 = 0
has two solutions:
x = 15/2 + √ 2225/4
or
x = 15/2 - √ 2225/4
Note that √ 2225/4 can be written as
√ 2225 / √ 4 which is √ 2225 / 2
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-15x-500 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -15
C = -500
Accordingly, B2 - 4AC =
225 - (-2000) =
2225
Applying the quadratic formula :
15 ± √ 2225
x = ——————
2
Can √ 2225 be simplified ?
Yes! The prime factorization of 2225 is
5•5•89
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 2225 = √ 5•5•89 =
± 5 • √ 89
√ 89 , rounded to 4 decimal digits, is 9.4340
So now we are looking at:
x = ( 15 ± 5 • 9.434 ) / 2
Two real solutions:
x =(15+√2225)/2=(15+5√ 89 )/2= 31.085
or:
x =(15-√2225)/2=(15-5√ 89 )/2= -16.085
Two solutions were found :
- x =(15-√2225)/2=(15-5√ 89 )/2= -16.085
- x =(15+√2225)/2=(15+5√ 89 )/2= 31.085
15x x^2
Simple and best practice solution for x^2-15x-2=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.
If it's not what You are looking for type in the equation solver your own equation and let us solve it.
Solution for x^2-15x-2=0 equation:
Simplifying x2 + -15x + -2 = 0 Reorder the terms: -2 + -15x + x2 = 0 Solving -2 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -15x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -15x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -15x + x2 = 0 + 2 -15x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -15x + x2 = 2 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 2 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 2 + 56.25 Combine like terms: 2 + 56.25 = 58.25 56.25 + -15x + x2 = 58.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + -7.5) equal to 7.632168761 and -7.632168761.
Subproblem 1
x + -7.5 = 7.632168761 Simplifying x + -7.5 = 7.632168761 Reorder the terms: -7.5 + x = 7.632168761 Solving -7.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.632168761 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.632168761 + 7.5 x = 7.632168761 + 7.5 Combine like terms: 7.632168761 + 7.5 = 15.132168761 x = 15.132168761 Simplifying x = 15.132168761Subproblem 2
x + -7.5 = -7.632168761 Simplifying x + -7.5 = -7.632168761 Reorder the terms: -7.5 + x = -7.632168761 Solving -7.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.632168761 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.632168761 + 7.5 x = -7.632168761 + 7.5 Combine like terms: -7.632168761 + 7.5 = -0.132168761 x = -0.132168761 Simplifying x = -0.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.132168761, -0.132168761}You can always share this solution
See similar equations:
| 1-5b-8b^2=0 || 4x^2+y^2-8x+4y+4=0 || X(x-3)=x+3 || 9+6k-8k^2=0 || 5+7x-6x^2=0 || 2x^2+7x+14=0 || 6a^2-5a-2=0 || 2x^2+7+14=0 || 6a^2-51-2=0 || r^2-8r=0 || 4y^2-y-3=0 || (2x^3*-7)(6x^3-6)=0 || 8m^3n^4-22m^5n^6= || -7x^2-66x-27=0 || (x-5)(x+1)=4 || 2+5*x=4x || 3r^2-2r-5=0 || -6y-5=7+9y || 3r^2-24-5=0 || 10r+8=58 || 72m^7n+24n= || 49m^5n^3+28mn^4= || a^2+13a-68=0 || 10m^3n^2-25m^2n^3= || 2s+9s+20=128 || 7p+9=8p+4 || 3(x-2)=-2x-16 || m^3n+9m^2n= || 4(2x+3u)-3(x-y)= || 9x^3+30x= || 45x^2-20x= || 2*N=12 |
Equations solver categories
Jack froze from his helplessness, he could not stop the men who raped his wife. And now I have to look at how his son will force his mother, fiercely a member of the master. He felt humiliated and he… liked it. I liked to obey someone else's will and see how his wife gives pleasure to unknown men, how she herself gets pleasure from fucking her son.
You will also be interested:
- Florida learners permit test
- Mac tools screwdriver set
- Floyd county magistrate court records
- Delta shower diverter stem replacement
- Meaning of merit in hindi
- The retreat at evans farms
Then. The mule could not stand it and shouted: "I also want a member, I want my ass to be fucked too!" And then the girlfriends changed roles, now Nastya accompanied Yulia's cock in the ass, so that I would not tear her anus with sharp movements. Yulina's ass was much elastic than her friend's, her anus walls squeezed my penis strongly, bringing tremendous pleasure.