-x^2-72x-80=0

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Solution for -x^2-72x-80=0 equation: 


Simplifying
-1x2 + -72x + -80 = 0

Reorder the terms:
-80 + -72x + -1x2 = 0

Solving
-80 + -72x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(80 + 72x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(80 + 72x + x2)' equal to zero and attempt to solve:

Simplifying
80 + 72x + x2 = 0

Solving
80 + 72x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-80' to each side of the equation.
80 + 72x + -80 + x2 = 0 + -80

Reorder the terms:
80 + -80 + 72x + x2 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + 72x + x2 = 0 + -80
72x + x2 = 0 + -80

Combine like terms: 0 + -80 = -80
72x + x2 = -80

The x term is 72x.  Take half its coefficient (36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
72x + 1296 + x2 = -80 + 1296

Reorder the terms:
1296 + 72x + x2 = -80 + 1296

Combine like terms: -80 + 1296 = 1216
1296 + 72x + x2 = 1216

Factor a perfect square on the left side:
(x + 36)(x + 36) = 1216

Calculate the square root of the right side: 34.871191548

Break this problem into two subproblems by setting 
(x + 36) equal to 34.871191548 and -34.871191548.


Subproblem 1
x + 36 = 34.871191548

Simplifying
x + 36 = 34.871191548

Reorder the terms:
36 + x = 34.871191548

Solving
36 + x = 34.871191548

Solving for variable 'x'.

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

Add '-36' to each side of the equation.
36 + -36 + x = 34.871191548 + -36

Combine like terms: 36 + -36 = 0
0 + x = 34.871191548 + -36
x = 34.871191548 + -36

Combine like terms: 34.871191548 + -36 = -1.128808452
x = -1.128808452

Simplifying
x = -1.128808452


Subproblem 2
x + 36 = -34.871191548

Simplifying
x + 36 = -34.871191548

Reorder the terms:
36 + x = -34.871191548

Solving
36 + x = -34.871191548

Solving for variable 'x'.

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

Add '-36' to each side of the equation.
36 + -36 + x = -34.871191548 + -36

Combine like terms: 36 + -36 = 0
0 + x = -34.871191548 + -36
x = -34.871191548 + -36

Combine like terms: -34.871191548 + -36 = -70.871191548
x = -70.871191548

Simplifying
x = -70.871191548


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.128808452, -70.871191548}
Solution
x = {-1.128808452, -70.871191548}

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