8x^2-128x+516=0

Solution for 8x^2-128x+516=0 equation:

Simplifying
8x2 + -128x + 516 = 0

Reorder the terms:
516 + -128x + 8x2 = 0

Solving
516 + -128x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(129 + -32x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(129 + -32x + 2x2)' equal to zero and attempt to solve:

Simplifying
129 + -32x + 2x2 = 0

Solving
129 + -32x + 2x2 = 0

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

Divide each side by '2'.
64.5 + -16x + x2 = 0

Move the constant term to the right:

Add '-64.5' to each side of the equation.
64.5 + -16x + -64.5 + x2 = 0 + -64.5

Reorder the terms:
64.5 + -64.5 + -16x + x2 = 0 + -64.5

Combine like terms: 64.5 + -64.5 = 0.0
0.0 + -16x + x2 = 0 + -64.5
-16x + x2 = 0 + -64.5

Combine like terms: 0 + -64.5 = -64.5
-16x + x2 = -64.5

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -64.5 + 64

Reorder the terms:
64 + -16x + x2 = -64.5 + 64

Combine like terms: -64.5 + 64 = -0.5
64 + -16x + x2 = -0.5

Factor a perfect square on the left side:
(x + -8)(x + -8) = -0.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.