0=4x^2-36x-72

Solution for 0=4x^2-36x-72 equation:

Simplifying
0 = 4x2 + -36x + -72

Reorder the terms:
0 = -72 + -36x + 4x2

Solving
0 = -72 + -36x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 72 = 72
72 + 36x + -4x2 = -72 + -36x + 4x2 + 72 + 36x + -4x2

Reorder the terms:
72 + 36x + -4x2 = -72 + 72 + -36x + 36x + 4x2 + -4x2

Combine like terms: -72 + 72 = 0
72 + 36x + -4x2 = 0 + -36x + 36x + 4x2 + -4x2
72 + 36x + -4x2 = -36x + 36x + 4x2 + -4x2

Combine like terms: -36x + 36x = 0
72 + 36x + -4x2 = 0 + 4x2 + -4x2
72 + 36x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
72 + 36x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + 9x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(18 + 9x + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + 9x + -1x2 = 0

Solving
18 + 9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-18 + -9x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -9x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -9x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -9x + x2 = 0 + 18
-9x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-9x + x2 = 18

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 18 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 18 + 20.25

Combine like terms: 18 + 20.25 = 38.25
20.25 + -9x + x2 = 38.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + -4.5) equal to 6.184658438 and -6.184658438.

Subproblem 1
x + -4.5 = 6.184658438

Simplifying
x + -4.5 = 6.184658438

Reorder the terms:
-4.5 + x = 6.184658438

Solving
-4.5 + x = 6.184658438

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 6.184658438 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 6.184658438 + 4.5
x = 6.184658438 + 4.5

Combine like terms: 6.184658438 + 4.5 = 10.684658438
x = 10.684658438

Simplifying
x = 10.684658438

Subproblem 2
x + -4.5 = -6.184658438

Simplifying
x + -4.5 = -6.184658438

Reorder the terms:
-4.5 + x = -6.184658438

Solving
-4.5 + x = -6.184658438

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -6.184658438 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -6.184658438 + 4.5
x = -6.184658438 + 4.5

Combine like terms: -6.184658438 + 4.5 = -1.684658438
x = -1.684658438

Simplifying
x = -1.684658438

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.684658438, -1.684658438}
Solution
x = {10.684658438, -1.684658438}