x^2-76x-8-80=0

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Solution for x^2-76x-8-80=0 equation: 


Simplifying
x2 + -76x + -8 + -80 = 0

Reorder the terms:
-8 + -80 + -76x + x2 = 0

Combine like terms: -8 + -80 = -88
-88 + -76x + x2 = 0

Solving
-88 + -76x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + -76x + 88 + x2 = 0 + 88

Reorder the terms:
-88 + 88 + -76x + x2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + -76x + x2 = 0 + 88
-76x + x2 = 0 + 88

Combine like terms: 0 + 88 = 88
-76x + x2 = 88

The x term is -76x.  Take half its coefficient (-38).
Square it (1444) and add it to both sides.

Add '1444' to each side of the equation.
-76x + 1444 + x2 = 88 + 1444

Reorder the terms:
1444 + -76x + x2 = 88 + 1444

Combine like terms: 88 + 1444 = 1532
1444 + -76x + x2 = 1532

Factor a perfect square on the left side:
(x + -38)(x + -38) = 1532

Calculate the square root of the right side: 39.140771582

Break this problem into two subproblems by setting 
(x + -38) equal to 39.140771582 and -39.140771582.


Subproblem 1
x + -38 = 39.140771582

Simplifying
x + -38 = 39.140771582

Reorder the terms:
-38 + x = 39.140771582

Solving
-38 + x = 39.140771582

Solving for variable 'x'.

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

Add '38' to each side of the equation.
-38 + 38 + x = 39.140771582 + 38

Combine like terms: -38 + 38 = 0
0 + x = 39.140771582 + 38
x = 39.140771582 + 38

Combine like terms: 39.140771582 + 38 = 77.140771582
x = 77.140771582

Simplifying
x = 77.140771582


Subproblem 2
x + -38 = -39.140771582

Simplifying
x + -38 = -39.140771582

Reorder the terms:
-38 + x = -39.140771582

Solving
-38 + x = -39.140771582

Solving for variable 'x'.

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

Add '38' to each side of the equation.
-38 + 38 + x = -39.140771582 + 38

Combine like terms: -38 + 38 = 0
0 + x = -39.140771582 + 38
x = -39.140771582 + 38

Combine like terms: -39.140771582 + 38 = -1.140771582
x = -1.140771582

Simplifying
x = -1.140771582


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {77.140771582, -1.140771582}

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