x^2+20x+26=0

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Solution for x^2+20x+26=0 equation: 


Simplifying
x2 + 20x + 26 = 0

Reorder the terms:
26 + 20x + x2 = 0

Solving
26 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + 20x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + 20x + x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 20x + x2 = 0 + -26
20x + x2 = 0 + -26

Combine like terms: 0 + -26 = -26
20x + x2 = -26

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -26 + 100

Reorder the terms:
100 + 20x + x2 = -26 + 100

Combine like terms: -26 + 100 = 74
100 + 20x + x2 = 74

Factor a perfect square on the left side:
(x + 10)(x + 10) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(x + 10) equal to 8.602325267 and -8.602325267.


Subproblem 1
x + 10 = 8.602325267

Simplifying
x + 10 = 8.602325267

Reorder the terms:
10 + x = 8.602325267

Solving
10 + x = 8.602325267

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 8.602325267 + -10

Combine like terms: 10 + -10 = 0
0 + x = 8.602325267 + -10
x = 8.602325267 + -10

Combine like terms: 8.602325267 + -10 = -1.397674733
x = -1.397674733

Simplifying
x = -1.397674733


Subproblem 2
x + 10 = -8.602325267

Simplifying
x + 10 = -8.602325267

Reorder the terms:
10 + x = -8.602325267

Solving
10 + x = -8.602325267

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -8.602325267 + -10

Combine like terms: 10 + -10 = 0
0 + x = -8.602325267 + -10
x = -8.602325267 + -10

Combine like terms: -8.602325267 + -10 = -18.602325267
x = -18.602325267

Simplifying
x = -18.602325267


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.397674733, -18.602325267}

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