x^2+37x+264=0

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Solution for x^2+37x+264=0 equation: 


Simplifying
x2 + 37x + 264 = 0

Reorder the terms:
264 + 37x + x2 = 0

Solving
264 + 37x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-264' to each side of the equation.
264 + 37x + -264 + x2 = 0 + -264

Reorder the terms:
264 + -264 + 37x + x2 = 0 + -264

Combine like terms: 264 + -264 = 0
0 + 37x + x2 = 0 + -264
37x + x2 = 0 + -264

Combine like terms: 0 + -264 = -264
37x + x2 = -264

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 = -264 + 342.25

Reorder the terms:
342.25 + 37x + x2 = -264 + 342.25

Combine like terms: -264 + 342.25 = 78.25
342.25 + 37x + x2 = 78.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x + 18.5) equal to 8.845903006 and -8.845903006.


Subproblem 1
x + 18.5 = 8.845903006

Simplifying
x + 18.5 = 8.845903006

Reorder the terms:
18.5 + x = 8.845903006

Solving
18.5 + x = 8.845903006

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 = 8.845903006 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = 8.845903006 + -18.5
x = 8.845903006 + -18.5

Combine like terms: 8.845903006 + -18.5 = -9.654096994
x = -9.654096994

Simplifying
x = -9.654096994


Subproblem 2
x + 18.5 = -8.845903006

Simplifying
x + 18.5 = -8.845903006

Reorder the terms:
18.5 + x = -8.845903006

Solving
18.5 + x = -8.845903006

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 = -8.845903006 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = -8.845903006 + -18.5
x = -8.845903006 + -18.5

Combine like terms: -8.845903006 + -18.5 = -27.345903006
x = -27.345903006

Simplifying
x = -27.345903006


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-9.654096994, -27.345903006}

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