8x^2-36x-36=0

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Solution for 8x^2-36x-36=0 equation: 


Simplifying
8x2 + -36x + -36 = 0

Reorder the terms:
-36 + -36x + 8x2 = 0

Solving
-36 + -36x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -9x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -9x + 2x2)' equal to zero and attempt to solve:

Simplifying
-9 + -9x + 2x2 = 0

Solving
-9 + -9x + 2x2 = 0

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

Divide each side by '2'.
-4.5 + -4.5x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -4.5x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -4.5x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -4.5x + x2 = 0 + 4.5
-4.5x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-4.5x + x2 = 4.5

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 4.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 4.5 + 5.0625

Combine like terms: 4.5 + 5.0625 = 9.5625
5.0625 + -4.5x + x2 = 9.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(x + -2.25) equal to 3.092329219 and -3.092329219.


Subproblem 1
x + -2.25 = 3.092329219

Simplifying
x + -2.25 = 3.092329219

Reorder the terms:
-2.25 + x = 3.092329219

Solving
-2.25 + x = 3.092329219

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 3.092329219 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 3.092329219 + 2.25
x = 3.092329219 + 2.25

Combine like terms: 3.092329219 + 2.25 = 5.342329219
x = 5.342329219

Simplifying
x = 5.342329219


Subproblem 2
x + -2.25 = -3.092329219

Simplifying
x + -2.25 = -3.092329219

Reorder the terms:
-2.25 + x = -3.092329219

Solving
-2.25 + x = -3.092329219

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -3.092329219 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -3.092329219 + 2.25
x = -3.092329219 + 2.25

Combine like terms: -3.092329219 + 2.25 = -0.842329219
x = -0.842329219

Simplifying
x = -0.842329219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.342329219, -0.842329219}
Solution
x = {5.342329219, -0.842329219}

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