36x^2-36x=63

Solution for 36x^2-36x=63 equation:

Simplifying
36x2 + -36x = 63

Reorder the terms:
-36x + 36x2 = 63

Solving
-36x + 36x2 = 63

Solving for variable 'x'.

Reorder the terms:
-63 + -36x + 36x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-63 + -36x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-7 + -4x + 4x2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-7 + -4x + 4x2)' equal to zero and attempt to solve:

Simplifying
-7 + -4x + 4x2 = 0

Solving
-7 + -4x + 4x2 = 0

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

Divide each side by '4'.
-1.75 + -1x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -1x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -1x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -1x + x2 = 0 + 1.75
-1x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-1x + x2 = 1.75

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1.75 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.75 + 0.25

Combine like terms: 1.75 + 0.25 = 2
0.25 + -1x + x2 = 2

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + -0.5 = 1.414213562

Simplifying
x + -0.5 = 1.414213562

Reorder the terms:
-0.5 + x = 1.414213562

Solving
-0.5 + x = 1.414213562

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.414213562 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.414213562 + 0.5
x = 1.414213562 + 0.5

Combine like terms: 1.414213562 + 0.5 = 1.914213562
x = 1.914213562

Simplifying
x = 1.914213562

Subproblem 2
x + -0.5 = -1.414213562

Simplifying
x + -0.5 = -1.414213562

Reorder the terms:
-0.5 + x = -1.414213562

Solving
-0.5 + x = -1.414213562

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.414213562 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.414213562 + 0.5
x = -1.414213562 + 0.5

Combine like terms: -1.414213562 + 0.5 = -0.914213562
x = -0.914213562

Simplifying
x = -0.914213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.914213562, -0.914213562}
Solution
x = {1.914213562, -0.914213562}