2x(x+36)=180

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Solution for 2x(x+36)=180 equation: 


Simplifying
2x(x + 36) = 180

Reorder the terms:
2x(36 + x) = 180
(36 * 2x + x * 2x) = 180
(72x + 2x2) = 180

Solving
72x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 72x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 72x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 36x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 36x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 36x + x2 = 0

Solving
-90 + 36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 36x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 36x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 36x + x2 = 0 + 90
36x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
36x + x2 = 90

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = 90 + 324

Reorder the terms:
324 + 36x + x2 = 90 + 324

Combine like terms: 90 + 324 = 414
324 + 36x + x2 = 414

Factor a perfect square on the left side:
(x + 18)(x + 18) = 414

Calculate the square root of the right side: 20.346989949

Break this problem into two subproblems by setting 
(x + 18) equal to 20.346989949 and -20.346989949.


Subproblem 1
x + 18 = 20.346989949

Simplifying
x + 18 = 20.346989949

Reorder the terms:
18 + x = 20.346989949

Solving
18 + x = 20.346989949

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = 20.346989949 + -18

Combine like terms: 18 + -18 = 0
0 + x = 20.346989949 + -18
x = 20.346989949 + -18

Combine like terms: 20.346989949 + -18 = 2.346989949
x = 2.346989949

Simplifying
x = 2.346989949


Subproblem 2
x + 18 = -20.346989949

Simplifying
x + 18 = -20.346989949

Reorder the terms:
18 + x = -20.346989949

Solving
18 + x = -20.346989949

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = -20.346989949 + -18

Combine like terms: 18 + -18 = 0
0 + x = -20.346989949 + -18
x = -20.346989949 + -18

Combine like terms: -20.346989949 + -18 = -38.346989949
x = -38.346989949

Simplifying
x = -38.346989949


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.346989949, -38.346989949}
Solution
x = {2.346989949, -38.346989949}

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