x^2+37x-180=0

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Solution for x^2+37x-180=0 equation: 


Simplifying
x2 + 37x + -180 = 0

Reorder the terms:
-180 + 37x + x2 = 0

Solving
-180 + 37x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 37x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 37x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 37x + x2 = 0 + 180
37x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
37x + x2 = 180

The x term is 37x.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37x + 342.25 + x2 = 180 + 342.25

Reorder the terms:
342.25 + 37x + x2 = 180 + 342.25

Combine like terms: 180 + 342.25 = 522.25
342.25 + 37x + x2 = 522.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 522.25

Calculate the square root of the right side: 22.852789764

Break this problem into two subproblems by setting 
(x + 18.5) equal to 22.852789764 and -22.852789764.


Subproblem 1
x + 18.5 = 22.852789764

Simplifying
x + 18.5 = 22.852789764

Reorder the terms:
18.5 + x = 22.852789764

Solving
18.5 + x = 22.852789764

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = 22.852789764 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = 22.852789764 + -18.5
x = 22.852789764 + -18.5

Combine like terms: 22.852789764 + -18.5 = 4.352789764
x = 4.352789764

Simplifying
x = 4.352789764


Subproblem 2
x + 18.5 = -22.852789764

Simplifying
x + 18.5 = -22.852789764

Reorder the terms:
18.5 + x = -22.852789764

Solving
18.5 + x = -22.852789764

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = -22.852789764 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = -22.852789764 + -18.5
x = -22.852789764 + -18.5

Combine like terms: -22.852789764 + -18.5 = -41.352789764
x = -41.352789764

Simplifying
x = -41.352789764


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.352789764, -41.352789764}

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