-x^2-18x-18=0

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Solution for -x^2-18x-18=0 equation: 


Simplifying
-1x2 + -18x + -18 = 0

Reorder the terms:
-18 + -18x + -1x2 = 0

Solving
-18 + -18x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 18x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(18 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
18 + 18x + x2 = 0

Solving
18 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 18x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 18x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 18x + x2 = 0 + -18
18x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
18x + x2 = -18

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -18 + 81

Reorder the terms:
81 + 18x + x2 = -18 + 81

Combine like terms: -18 + 81 = 63
81 + 18x + x2 = 63

Factor a perfect square on the left side:
(x + 9)(x + 9) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + 9) equal to 7.937253933 and -7.937253933.


Subproblem 1
x + 9 = 7.937253933

Simplifying
x + 9 = 7.937253933

Reorder the terms:
9 + x = 7.937253933

Solving
9 + x = 7.937253933

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 7.937253933 + -9

Combine like terms: 9 + -9 = 0
0 + x = 7.937253933 + -9
x = 7.937253933 + -9

Combine like terms: 7.937253933 + -9 = -1.062746067
x = -1.062746067

Simplifying
x = -1.062746067


Subproblem 2
x + 9 = -7.937253933

Simplifying
x + 9 = -7.937253933

Reorder the terms:
9 + x = -7.937253933

Solving
9 + x = -7.937253933

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -7.937253933 + -9

Combine like terms: 9 + -9 = 0
0 + x = -7.937253933 + -9
x = -7.937253933 + -9

Combine like terms: -7.937253933 + -9 = -16.937253933
x = -16.937253933

Simplifying
x = -16.937253933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.062746067, -16.937253933}
Solution
x = {-1.062746067, -16.937253933}

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