x^2+26x+85=0

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Solution for x^2+26x+85=0 equation: 


Simplifying
x2 + 26x + 85 = 0

Reorder the terms:
85 + 26x + x2 = 0

Solving
85 + 26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-85' to each side of the equation.
85 + 26x + -85 + x2 = 0 + -85

Reorder the terms:
85 + -85 + 26x + x2 = 0 + -85

Combine like terms: 85 + -85 = 0
0 + 26x + x2 = 0 + -85
26x + x2 = 0 + -85

Combine like terms: 0 + -85 = -85
26x + x2 = -85

The x term is 26x.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26x + 169 + x2 = -85 + 169

Reorder the terms:
169 + 26x + x2 = -85 + 169

Combine like terms: -85 + 169 = 84
169 + 26x + x2 = 84

Factor a perfect square on the left side:
(x + 13)(x + 13) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + 13) equal to 9.16515139 and -9.16515139.


Subproblem 1
x + 13 = 9.16515139

Simplifying
x + 13 = 9.16515139

Reorder the terms:
13 + x = 9.16515139

Solving
13 + x = 9.16515139

Solving for variable 'x'.

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

Add '-13' to each side of the equation.
13 + -13 + x = 9.16515139 + -13

Combine like terms: 13 + -13 = 0
0 + x = 9.16515139 + -13
x = 9.16515139 + -13

Combine like terms: 9.16515139 + -13 = -3.83484861
x = -3.83484861

Simplifying
x = -3.83484861


Subproblem 2
x + 13 = -9.16515139

Simplifying
x + 13 = -9.16515139

Reorder the terms:
13 + x = -9.16515139

Solving
13 + x = -9.16515139

Solving for variable 'x'.

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

Add '-13' to each side of the equation.
13 + -13 + x = -9.16515139 + -13

Combine like terms: 13 + -13 = 0
0 + x = -9.16515139 + -13
x = -9.16515139 + -13

Combine like terms: -9.16515139 + -13 = -22.16515139
x = -22.16515139

Simplifying
x = -22.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.83484861, -22.16515139}

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