-8x^2+130x-136=0

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Solution for -8x^2+130x-136=0 equation:


Simplifying
-8x2 + 130x + -136 = 0

Reorder the terms:
-136 + 130x + -8x2 = 0

Solving
-136 + 130x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + 65x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-68 + 65x + -4x2)' equal to zero and attempt to solve:

Simplifying
-68 + 65x + -4x2 = 0

Solving
-68 + 65x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
17 + -16.25x + x2 = 0

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -16.25x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + -16.25x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -16.25x + x2 = 0 + -17
-16.25x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
-16.25x + x2 = -17

The x term is -16.25x.  Take half its coefficient (-8.125).
Square it (66.015625) and add it to both sides.

Add '66.015625' to each side of the equation.
-16.25x + 66.015625 + x2 = -17 + 66.015625

Reorder the terms:
66.015625 + -16.25x + x2 = -17 + 66.015625

Combine like terms: -17 + 66.015625 = 49.015625
66.015625 + -16.25x + x2 = 49.015625

Factor a perfect square on the left side:
(x + -8.125)(x + -8.125) = 49.015625

Calculate the square root of the right side: 7.001115982

Break this problem into two subproblems by setting 
(x + -8.125) equal to 7.001115982 and -7.001115982.


Subproblem 1
x + -8.125 = 7.001115982

Simplifying
x + -8.125 = 7.001115982

Reorder the terms:
-8.125 + x = 7.001115982

Solving
-8.125 + x = 7.001115982

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8.125' to each side of the equation.
-8.125 + 8.125 + x = 7.001115982 + 8.125

Combine like terms: -8.125 + 8.125 = 0.000
0.000 + x = 7.001115982 + 8.125
x = 7.001115982 + 8.125

Combine like terms: 7.001115982 + 8.125 = 15.126115982
x = 15.126115982

Simplifying
x = 15.126115982


Subproblem 2
x + -8.125 = -7.001115982

Simplifying
x + -8.125 = -7.001115982

Reorder the terms:
-8.125 + x = -7.001115982

Solving
-8.125 + x = -7.001115982

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8.125' to each side of the equation.
-8.125 + 8.125 + x = -7.001115982 + 8.125

Combine like terms: -8.125 + 8.125 = 0.000
0.000 + x = -7.001115982 + 8.125
x = -7.001115982 + 8.125

Combine like terms: -7.001115982 + 8.125 = 1.123884018
x = 1.123884018

Simplifying
x = 1.123884018


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.126115982, 1.123884018}
Solution
x = {15.126115982, 1.123884018}

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