x^2+30x+117=0

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Solution for x^2+30x+117=0 equation: 


Simplifying
x2 + 30x + 117 = 0

Reorder the terms:
117 + 30x + x2 = 0

Solving
117 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-117' to each side of the equation.
117 + 30x + -117 + x2 = 0 + -117

Reorder the terms:
117 + -117 + 30x + x2 = 0 + -117

Combine like terms: 117 + -117 = 0
0 + 30x + x2 = 0 + -117
30x + x2 = 0 + -117

Combine like terms: 0 + -117 = -117
30x + x2 = -117

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -117 + 225

Reorder the terms:
225 + 30x + x2 = -117 + 225

Combine like terms: -117 + 225 = 108
225 + 30x + x2 = 108

Factor a perfect square on the left side:
(x + 15)(x + 15) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(x + 15) equal to 10.392304845 and -10.392304845.


Subproblem 1
x + 15 = 10.392304845

Simplifying
x + 15 = 10.392304845

Reorder the terms:
15 + x = 10.392304845

Solving
15 + x = 10.392304845

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 10.392304845 + -15

Combine like terms: 15 + -15 = 0
0 + x = 10.392304845 + -15
x = 10.392304845 + -15

Combine like terms: 10.392304845 + -15 = -4.607695155
x = -4.607695155

Simplifying
x = -4.607695155


Subproblem 2
x + 15 = -10.392304845

Simplifying
x + 15 = -10.392304845

Reorder the terms:
15 + x = -10.392304845

Solving
15 + x = -10.392304845

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -10.392304845 + -15

Combine like terms: 15 + -15 = 0
0 + x = -10.392304845 + -15
x = -10.392304845 + -15

Combine like terms: -10.392304845 + -15 = -25.392304845
x = -25.392304845

Simplifying
x = -25.392304845


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.607695155, -25.392304845}

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