4x^2+36x-180=0

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Solution for 4x^2+36x-180=0 equation: 


Simplifying
4x2 + 36x + -180 = 0

Reorder the terms:
-180 + 36x + 4x2 = 0

Solving
-180 + 36x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 9x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 9x + x2 = 0

Solving
-45 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 9x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 9x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 9x + x2 = 0 + 45
9x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
9x + x2 = 45

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 = 45 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 45 + 20.25

Combine like terms: 45 + 20.25 = 65.25
20.25 + 9x + x2 = 65.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(x + 4.5) equal to 8.077747211 and -8.077747211.


Subproblem 1
x + 4.5 = 8.077747211

Simplifying
x + 4.5 = 8.077747211

Reorder the terms:
4.5 + x = 8.077747211

Solving
4.5 + x = 8.077747211

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 = 8.077747211 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 8.077747211 + -4.5
x = 8.077747211 + -4.5

Combine like terms: 8.077747211 + -4.5 = 3.577747211
x = 3.577747211

Simplifying
x = 3.577747211


Subproblem 2
x + 4.5 = -8.077747211

Simplifying
x + 4.5 = -8.077747211

Reorder the terms:
4.5 + x = -8.077747211

Solving
4.5 + x = -8.077747211

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 = -8.077747211 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -8.077747211 + -4.5
x = -8.077747211 + -4.5

Combine like terms: -8.077747211 + -4.5 = -12.577747211
x = -12.577747211

Simplifying
x = -12.577747211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.577747211, -12.577747211}
Solution
x = {3.577747211, -12.577747211}

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