100x^2+64x-64=0

Solution for 100x^2+64x-64=0 equation:

Simplifying
100x2 + 64x + -64 = 0

Reorder the terms:
-64 + 64x + 100x2 = 0

Solving
-64 + 64x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 16x + 25x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-16 + 16x + 25x2)' equal to zero and attempt to solve:

Simplifying
-16 + 16x + 25x2 = 0

Solving
-16 + 16x + 25x2 = 0

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

Divide each side by '25'.
-0.64 + 0.64x + x2 = 0

Move the constant term to the right:

Add '0.64' to each side of the equation.
-0.64 + 0.64x + 0.64 + x2 = 0 + 0.64

Reorder the terms:
-0.64 + 0.64 + 0.64x + x2 = 0 + 0.64

Combine like terms: -0.64 + 0.64 = 0.00
0.00 + 0.64x + x2 = 0 + 0.64
0.64x + x2 = 0 + 0.64

Combine like terms: 0 + 0.64 = 0.64
0.64x + x2 = 0.64

The x term is 0.64x.  Take half its coefficient (0.32).
Square it (0.1024) and add it to both sides.

Add '0.1024' to each side of the equation.
0.64x + 0.1024 + x2 = 0.64 + 0.1024

Reorder the terms:
0.1024 + 0.64x + x2 = 0.64 + 0.1024

Combine like terms: 0.64 + 0.1024 = 0.7424
0.1024 + 0.64x + x2 = 0.7424

Factor a perfect square on the left side:
(x + 0.32)(x + 0.32) = 0.7424

Calculate the square root of the right side: 0.861626369

Break this problem into two subproblems by setting 
(x + 0.32) equal to 0.861626369 and -0.861626369.

Subproblem 1
x + 0.32 = 0.861626369

Simplifying
x + 0.32 = 0.861626369

Reorder the terms:
0.32 + x = 0.861626369

Solving
0.32 + x = 0.861626369

Solving for variable 'x'.

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

Add '-0.32' to each side of the equation.
0.32 + -0.32 + x = 0.861626369 + -0.32

Combine like terms: 0.32 + -0.32 = 0.00
0.00 + x = 0.861626369 + -0.32
x = 0.861626369 + -0.32

Combine like terms: 0.861626369 + -0.32 = 0.541626369
x = 0.541626369

Simplifying
x = 0.541626369

Subproblem 2
x + 0.32 = -0.861626369

Simplifying
x + 0.32 = -0.861626369

Reorder the terms:
0.32 + x = -0.861626369

Solving
0.32 + x = -0.861626369

Solving for variable 'x'.

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

Add '-0.32' to each side of the equation.
0.32 + -0.32 + x = -0.861626369 + -0.32

Combine like terms: 0.32 + -0.32 = 0.00
0.00 + x = -0.861626369 + -0.32
x = -0.861626369 + -0.32

Combine like terms: -0.861626369 + -0.32 = -1.181626369
x = -1.181626369

Simplifying
x = -1.181626369

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.541626369, -1.181626369}
Solution
x = {0.541626369, -1.181626369}