x^2+15x-26=0

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Solution for x^2+15x-26=0 equation: 


Simplifying
x2 + 15x + -26 = 0

Reorder the terms:
-26 + 15x + x2 = 0

Solving
-26 + 15x + 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 + 15x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + 15x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 15x + x2 = 0 + 26
15x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
15x + x2 = 26

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 26 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 26 + 56.25

Combine like terms: 26 + 56.25 = 82.25
56.25 + 15x + x2 = 82.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(x + 7.5) equal to 9.069178574 and -9.069178574.


Subproblem 1
x + 7.5 = 9.069178574

Simplifying
x + 7.5 = 9.069178574

Reorder the terms:
7.5 + x = 9.069178574

Solving
7.5 + x = 9.069178574

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 9.069178574 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 9.069178574 + -7.5
x = 9.069178574 + -7.5

Combine like terms: 9.069178574 + -7.5 = 1.569178574
x = 1.569178574

Simplifying
x = 1.569178574


Subproblem 2
x + 7.5 = -9.069178574

Simplifying
x + 7.5 = -9.069178574

Reorder the terms:
7.5 + x = -9.069178574

Solving
7.5 + x = -9.069178574

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -9.069178574 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -9.069178574 + -7.5
x = -9.069178574 + -7.5

Combine like terms: -9.069178574 + -7.5 = -16.569178574
x = -16.569178574

Simplifying
x = -16.569178574


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.569178574, -16.569178574}

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