-(x^2+12x+30)=0

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Solution for -(x^2+12x+30)=0 equation: 


Simplifying
-1(x2 + 12x + 30) = 0

Reorder the terms:
-1(30 + 12x + x2) = 0
(30 * -1 + 12x * -1 + x2 * -1) = 0
(-30 + -12x + -1x2) = 0

Solving
-30 + -12x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 12x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(30 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
30 + 12x + x2 = 0

Solving
30 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 12x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 12x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 12x + x2 = 0 + -30
12x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
12x + x2 = -30

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -30 + 36

Reorder the terms:
36 + 12x + x2 = -30 + 36

Combine like terms: -30 + 36 = 6
36 + 12x + x2 = 6

Factor a perfect square on the left side:
(x + 6)(x + 6) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 6) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 6 = 2.449489743

Simplifying
x + 6 = 2.449489743

Reorder the terms:
6 + x = 2.449489743

Solving
6 + x = 2.449489743

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 2.449489743 + -6

Combine like terms: 6 + -6 = 0
0 + x = 2.449489743 + -6
x = 2.449489743 + -6

Combine like terms: 2.449489743 + -6 = -3.550510257
x = -3.550510257

Simplifying
x = -3.550510257


Subproblem 2
x + 6 = -2.449489743

Simplifying
x + 6 = -2.449489743

Reorder the terms:
6 + x = -2.449489743

Solving
6 + x = -2.449489743

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -2.449489743 + -6

Combine like terms: 6 + -6 = 0
0 + x = -2.449489743 + -6
x = -2.449489743 + -6

Combine like terms: -2.449489743 + -6 = -8.449489743
x = -8.449489743

Simplifying
x = -8.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.550510257, -8.449489743}
Solution
x = {-3.550510257, -8.449489743}

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