x^2+26x+40=0

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Solution for x^2+26x+40=0 equation: 


Simplifying
x2 + 26x + 40 = 0

Reorder the terms:
40 + 26x + x2 = 0

Solving
40 + 26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 26x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 26x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 26x + x2 = 0 + -40
26x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
26x + x2 = -40

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 = -40 + 169

Reorder the terms:
169 + 26x + x2 = -40 + 169

Combine like terms: -40 + 169 = 129
169 + 26x + x2 = 129

Factor a perfect square on the left side:
(x + 13)(x + 13) = 129

Calculate the square root of the right side: 11.357816692

Break this problem into two subproblems by setting 
(x + 13) equal to 11.357816692 and -11.357816692.


Subproblem 1
x + 13 = 11.357816692

Simplifying
x + 13 = 11.357816692

Reorder the terms:
13 + x = 11.357816692

Solving
13 + x = 11.357816692

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 = 11.357816692 + -13

Combine like terms: 13 + -13 = 0
0 + x = 11.357816692 + -13
x = 11.357816692 + -13

Combine like terms: 11.357816692 + -13 = -1.642183308
x = -1.642183308

Simplifying
x = -1.642183308


Subproblem 2
x + 13 = -11.357816692

Simplifying
x + 13 = -11.357816692

Reorder the terms:
13 + x = -11.357816692

Solving
13 + x = -11.357816692

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 = -11.357816692 + -13

Combine like terms: 13 + -13 = 0
0 + x = -11.357816692 + -13
x = -11.357816692 + -13

Combine like terms: -11.357816692 + -13 = -24.357816692
x = -24.357816692

Simplifying
x = -24.357816692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.642183308, -24.357816692}

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