36x^2-684x-648=0

Solution for 36x^2-684x-648=0 equation:

Simplifying
36x2 + -684x + -648 = 0

Reorder the terms:
-648 + -684x + 36x2 = 0

Solving
-648 + -684x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '36'.
36(-18 + -19x + x2) = 0

Ignore the factor 36.
Subproblem 1
Set the factor '(-18 + -19x + x2)' equal to zero and attempt to solve:

Simplifying
-18 + -19x + x2 = 0

Solving
-18 + -19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -19x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -19x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -19x + x2 = 0 + 18
-19x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-19x + x2 = 18

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = 18 + 90.25

Reorder the terms:
90.25 + -19x + x2 = 18 + 90.25

Combine like terms: 18 + 90.25 = 108.25
90.25 + -19x + x2 = 108.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 108.25

Calculate the square root of the right side: 10.404326023

Break this problem into two subproblems by setting 
(x + -9.5) equal to 10.404326023 and -10.404326023.

Subproblem 1
x + -9.5 = 10.404326023

Simplifying
x + -9.5 = 10.404326023

Reorder the terms:
-9.5 + x = 10.404326023

Solving
-9.5 + x = 10.404326023

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 10.404326023 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 10.404326023 + 9.5
x = 10.404326023 + 9.5

Combine like terms: 10.404326023 + 9.5 = 19.904326023
x = 19.904326023

Simplifying
x = 19.904326023

Subproblem 2
x + -9.5 = -10.404326023

Simplifying
x + -9.5 = -10.404326023

Reorder the terms:
-9.5 + x = -10.404326023

Solving
-9.5 + x = -10.404326023

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -10.404326023 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -10.404326023 + 9.5
x = -10.404326023 + 9.5

Combine like terms: -10.404326023 + 9.5 = -0.904326023
x = -0.904326023

Simplifying
x = -0.904326023

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.904326023, -0.904326023}
Solution
x = {19.904326023, -0.904326023}