8x^2-132x+76=0

Solution for 8x^2-132x+76=0 equation:

Simplifying
8x2 + -132x + 76 = 0

Reorder the terms:
76 + -132x + 8x2 = 0

Solving
76 + -132x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(19 + -33x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(19 + -33x + 2x2)' equal to zero and attempt to solve:

Simplifying
19 + -33x + 2x2 = 0

Solving
19 + -33x + 2x2 = 0

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

Divide each side by '2'.
9.5 + -16.5x + x2 = 0

Move the constant term to the right:

Add '-9.5' to each side of the equation.
9.5 + -16.5x + -9.5 + x2 = 0 + -9.5

Reorder the terms:
9.5 + -9.5 + -16.5x + x2 = 0 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + -16.5x + x2 = 0 + -9.5
-16.5x + x2 = 0 + -9.5

Combine like terms: 0 + -9.5 = -9.5
-16.5x + x2 = -9.5

The x term is -16.5x.  Take half its coefficient (-8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
-16.5x + 68.0625 + x2 = -9.5 + 68.0625

Reorder the terms:
68.0625 + -16.5x + x2 = -9.5 + 68.0625

Combine like terms: -9.5 + 68.0625 = 58.5625
68.0625 + -16.5x + x2 = 58.5625

Factor a perfect square on the left side:
(x + -8.25)(x + -8.25) = 58.5625

Calculate the square root of the right side: 7.652613933

Break this problem into two subproblems by setting 
(x + -8.25) equal to 7.652613933 and -7.652613933.

Subproblem 1
x + -8.25 = 7.652613933

Simplifying
x + -8.25 = 7.652613933

Reorder the terms:
-8.25 + x = 7.652613933

Solving
-8.25 + x = 7.652613933

Solving for variable 'x'.

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

Add '8.25' to each side of the equation.
-8.25 + 8.25 + x = 7.652613933 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = 7.652613933 + 8.25
x = 7.652613933 + 8.25

Combine like terms: 7.652613933 + 8.25 = 15.902613933
x = 15.902613933

Simplifying
x = 15.902613933

Subproblem 2
x + -8.25 = -7.652613933

Simplifying
x + -8.25 = -7.652613933

Reorder the terms:
-8.25 + x = -7.652613933

Solving
-8.25 + x = -7.652613933

Solving for variable 'x'.

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

Add '8.25' to each side of the equation.
-8.25 + 8.25 + x = -7.652613933 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = -7.652613933 + 8.25
x = -7.652613933 + 8.25

Combine like terms: -7.652613933 + 8.25 = 0.597386067
x = 0.597386067

Simplifying
x = 0.597386067

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.902613933, 0.597386067}
Solution
x = {15.902613933, 0.597386067}