x^2+26x-20=0

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


Simplifying
x2 + 26x + -20 = 0

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

Solving
-20 + 26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 20 + 169

Reorder the terms:
169 + 26x + x2 = 20 + 169

Combine like terms: 20 + 169 = 189
169 + 26x + x2 = 189

Factor a perfect square on the left side:
(x + 13)(x + 13) = 189

Calculate the square root of the right side: 13.747727085

Break this problem into two subproblems by setting 
(x + 13) equal to 13.747727085 and -13.747727085.


Subproblem 1
x + 13 = 13.747727085

Simplifying
x + 13 = 13.747727085

Reorder the terms:
13 + x = 13.747727085

Solving
13 + x = 13.747727085

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 = 13.747727085 + -13

Combine like terms: 13 + -13 = 0
0 + x = 13.747727085 + -13
x = 13.747727085 + -13

Combine like terms: 13.747727085 + -13 = 0.747727085
x = 0.747727085

Simplifying
x = 0.747727085


Subproblem 2
x + 13 = -13.747727085

Simplifying
x + 13 = -13.747727085

Reorder the terms:
13 + x = -13.747727085

Solving
13 + x = -13.747727085

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 = -13.747727085 + -13

Combine like terms: 13 + -13 = 0
0 + x = -13.747727085 + -13
x = -13.747727085 + -13

Combine like terms: -13.747727085 + -13 = -26.747727085
x = -26.747727085

Simplifying
x = -26.747727085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.747727085, -26.747727085}

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