x^2+76x+80=0

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Solution for x^2+76x+80=0 equation: 


Simplifying
x2 + 76x + 80 = 0

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

Solving
80 + 76x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-80' to each side of the equation.
80 + 76x + -80 + x2 = 0 + -80

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

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

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

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 = -80 + 1444

Reorder the terms:
1444 + 76x + x2 = -80 + 1444

Combine like terms: -80 + 1444 = 1364
1444 + 76x + x2 = 1364

Factor a perfect square on the left side:
(x + 38)(x + 38) = 1364

Calculate the square root of the right side: 36.932370625

Break this problem into two subproblems by setting 
(x + 38) equal to 36.932370625 and -36.932370625.


Subproblem 1
x + 38 = 36.932370625

Simplifying
x + 38 = 36.932370625

Reorder the terms:
38 + x = 36.932370625

Solving
38 + x = 36.932370625

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 = 36.932370625 + -38

Combine like terms: 38 + -38 = 0
0 + x = 36.932370625 + -38
x = 36.932370625 + -38

Combine like terms: 36.932370625 + -38 = -1.067629375
x = -1.067629375

Simplifying
x = -1.067629375


Subproblem 2
x + 38 = -36.932370625

Simplifying
x + 38 = -36.932370625

Reorder the terms:
38 + x = -36.932370625

Solving
38 + x = -36.932370625

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 = -36.932370625 + -38

Combine like terms: 38 + -38 = 0
0 + x = -36.932370625 + -38
x = -36.932370625 + -38

Combine like terms: -36.932370625 + -38 = -74.932370625
x = -74.932370625

Simplifying
x = -74.932370625


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.067629375, -74.932370625}

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