x^2+80x+11=0

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Solution for x^2+80x+11=0 equation: 


Simplifying
x2 + 80x + 11 = 0

Reorder the terms:
11 + 80x + x2 = 0

Solving
11 + 80x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 80x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 80x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 80x + x2 = 0 + -11
80x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
80x + x2 = -11

The x term is 80x.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80x + 1600 + x2 = -11 + 1600

Reorder the terms:
1600 + 80x + x2 = -11 + 1600

Combine like terms: -11 + 1600 = 1589
1600 + 80x + x2 = 1589

Factor a perfect square on the left side:
(x + 40)(x + 40) = 1589

Calculate the square root of the right side: 39.862262856

Break this problem into two subproblems by setting 
(x + 40) equal to 39.862262856 and -39.862262856.


Subproblem 1
x + 40 = 39.862262856

Simplifying
x + 40 = 39.862262856

Reorder the terms:
40 + x = 39.862262856

Solving
40 + x = 39.862262856

Solving for variable 'x'.

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

Add '-40' to each side of the equation.
40 + -40 + x = 39.862262856 + -40

Combine like terms: 40 + -40 = 0
0 + x = 39.862262856 + -40
x = 39.862262856 + -40

Combine like terms: 39.862262856 + -40 = -0.137737144
x = -0.137737144

Simplifying
x = -0.137737144


Subproblem 2
x + 40 = -39.862262856

Simplifying
x + 40 = -39.862262856

Reorder the terms:
40 + x = -39.862262856

Solving
40 + x = -39.862262856

Solving for variable 'x'.

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

Add '-40' to each side of the equation.
40 + -40 + x = -39.862262856 + -40

Combine like terms: 40 + -40 = 0
0 + x = -39.862262856 + -40
x = -39.862262856 + -40

Combine like terms: -39.862262856 + -40 = -79.862262856
x = -79.862262856

Simplifying
x = -79.862262856


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.137737144, -79.862262856}

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