x^2+81x+81=0

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Solution for x^2+81x+81=0 equation: 


Simplifying
x2 + 81x + 81 = 0

Reorder the terms:
81 + 81x + x2 = 0

Solving
81 + 81x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + 81x + -81 + x2 = 0 + -81

Reorder the terms:
81 + -81 + 81x + x2 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + 81x + x2 = 0 + -81
81x + x2 = 0 + -81

Combine like terms: 0 + -81 = -81
81x + x2 = -81

The x term is 81x.  Take half its coefficient (40.5).
Square it (1640.25) and add it to both sides.

Add '1640.25' to each side of the equation.
81x + 1640.25 + x2 = -81 + 1640.25

Reorder the terms:
1640.25 + 81x + x2 = -81 + 1640.25

Combine like terms: -81 + 1640.25 = 1559.25
1640.25 + 81x + x2 = 1559.25

Factor a perfect square on the left side:
(x + 40.5)(x + 40.5) = 1559.25

Calculate the square root of the right side: 39.487339743

Break this problem into two subproblems by setting 
(x + 40.5) equal to 39.487339743 and -39.487339743.


Subproblem 1
x + 40.5 = 39.487339743

Simplifying
x + 40.5 = 39.487339743

Reorder the terms:
40.5 + x = 39.487339743

Solving
40.5 + x = 39.487339743

Solving for variable 'x'.

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

Add '-40.5' to each side of the equation.
40.5 + -40.5 + x = 39.487339743 + -40.5

Combine like terms: 40.5 + -40.5 = 0.0
0.0 + x = 39.487339743 + -40.5
x = 39.487339743 + -40.5

Combine like terms: 39.487339743 + -40.5 = -1.012660257
x = -1.012660257

Simplifying
x = -1.012660257


Subproblem 2
x + 40.5 = -39.487339743

Simplifying
x + 40.5 = -39.487339743

Reorder the terms:
40.5 + x = -39.487339743

Solving
40.5 + x = -39.487339743

Solving for variable 'x'.

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

Add '-40.5' to each side of the equation.
40.5 + -40.5 + x = -39.487339743 + -40.5

Combine like terms: 40.5 + -40.5 = 0.0
0.0 + x = -39.487339743 + -40.5
x = -39.487339743 + -40.5

Combine like terms: -39.487339743 + -40.5 = -79.987339743
x = -79.987339743

Simplifying
x = -79.987339743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.012660257, -79.987339743}

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