2x^2+26x-13=0

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Solution for 2x^2+26x-13=0 equation: 


Simplifying
2x2 + 26x + -13 = 0

Reorder the terms:
-13 + 26x + 2x2 = 0

Solving
-13 + 26x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-6.5 + 13x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 13x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 13x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 13x + x2 = 0 + 6.5
13x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
13x + x2 = 6.5

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 6.5 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 6.5 + 42.25

Combine like terms: 6.5 + 42.25 = 48.75
42.25 + 13x + x2 = 48.75

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 48.75

Calculate the square root of the right side: 6.982120022

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.982120022 and -6.982120022.


Subproblem 1
x + 6.5 = 6.982120022

Simplifying
x + 6.5 = 6.982120022

Reorder the terms:
6.5 + x = 6.982120022

Solving
6.5 + x = 6.982120022

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.982120022 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.982120022 + -6.5
x = 6.982120022 + -6.5

Combine like terms: 6.982120022 + -6.5 = 0.482120022
x = 0.482120022

Simplifying
x = 0.482120022


Subproblem 2
x + 6.5 = -6.982120022

Simplifying
x + 6.5 = -6.982120022

Reorder the terms:
6.5 + x = -6.982120022

Solving
6.5 + x = -6.982120022

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.982120022 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.982120022 + -6.5
x = -6.982120022 + -6.5

Combine like terms: -6.982120022 + -6.5 = -13.482120022
x = -13.482120022

Simplifying
x = -13.482120022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.482120022, -13.482120022}

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