13x^2+26x-23=0

Solution for 13x^2+26x-23=0 equation:

Simplifying
13x2 + 26x + -23 = 0

Reorder the terms:
-23 + 26x + 13x2 = 0

Solving
-23 + 26x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-1.769230769 + 2x + x2 = 0

Move the constant term to the right:

Add '1.769230769' to each side of the equation.
-1.769230769 + 2x + 1.769230769 + x2 = 0 + 1.769230769

Reorder the terms:
-1.769230769 + 1.769230769 + 2x + x2 = 0 + 1.769230769

Combine like terms: -1.769230769 + 1.769230769 = 0.000000000
0.000000000 + 2x + x2 = 0 + 1.769230769
2x + x2 = 0 + 1.769230769

Combine like terms: 0 + 1.769230769 = 1.769230769
2x + x2 = 1.769230769

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.769230769 + 1

Reorder the terms:
1 + 2x + x2 = 1.769230769 + 1

Combine like terms: 1.769230769 + 1 = 2.769230769
1 + 2x + x2 = 2.769230769

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.769230769

Calculate the square root of the right side: 1.664100589

Break this problem into two subproblems by setting 
(x + 1) equal to 1.664100589 and -1.664100589.

Subproblem 1
x + 1 = 1.664100589

Simplifying
x + 1 = 1.664100589

Reorder the terms:
1 + x = 1.664100589

Solving
1 + x = 1.664100589

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.664100589 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.664100589 + -1
x = 1.664100589 + -1

Combine like terms: 1.664100589 + -1 = 0.664100589
x = 0.664100589

Simplifying
x = 0.664100589

Subproblem 2
x + 1 = -1.664100589

Simplifying
x + 1 = -1.664100589

Reorder the terms:
1 + x = -1.664100589

Solving
1 + x = -1.664100589

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.664100589 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.664100589 + -1
x = -1.664100589 + -1

Combine like terms: -1.664100589 + -1 = -2.664100589
x = -2.664100589

Simplifying
x = -2.664100589

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.664100589, -2.664100589}