-x^2-88x-12=0

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Solution for -x^2-88x-12=0 equation: 


Simplifying
-1x2 + -88x + -12 = 0

Reorder the terms:
-12 + -88x + -1x2 = 0

Solving
-12 + -88x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 88x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(12 + 88x + x2)' equal to zero and attempt to solve:

Simplifying
12 + 88x + x2 = 0

Solving
12 + 88x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 88x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 88x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 88x + x2 = 0 + -12
88x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
88x + x2 = -12

The x term is 88x.  Take half its coefficient (44).
Square it (1936) and add it to both sides.

Add '1936' to each side of the equation.
88x + 1936 + x2 = -12 + 1936

Reorder the terms:
1936 + 88x + x2 = -12 + 1936

Combine like terms: -12 + 1936 = 1924
1936 + 88x + x2 = 1924

Factor a perfect square on the left side:
(x + 44)(x + 44) = 1924

Calculate the square root of the right side: 43.863424399

Break this problem into two subproblems by setting 
(x + 44) equal to 43.863424399 and -43.863424399.


Subproblem 1
x + 44 = 43.863424399

Simplifying
x + 44 = 43.863424399

Reorder the terms:
44 + x = 43.863424399

Solving
44 + x = 43.863424399

Solving for variable 'x'.

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

Add '-44' to each side of the equation.
44 + -44 + x = 43.863424399 + -44

Combine like terms: 44 + -44 = 0
0 + x = 43.863424399 + -44
x = 43.863424399 + -44

Combine like terms: 43.863424399 + -44 = -0.136575601
x = -0.136575601

Simplifying
x = -0.136575601


Subproblem 2
x + 44 = -43.863424399

Simplifying
x + 44 = -43.863424399

Reorder the terms:
44 + x = -43.863424399

Solving
44 + x = -43.863424399

Solving for variable 'x'.

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

Add '-44' to each side of the equation.
44 + -44 + x = -43.863424399 + -44

Combine like terms: 44 + -44 = 0
0 + x = -43.863424399 + -44
x = -43.863424399 + -44

Combine like terms: -43.863424399 + -44 = -87.863424399
x = -87.863424399

Simplifying
x = -87.863424399


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.136575601, -87.863424399}
Solution
x = {-0.136575601, -87.863424399}

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