2x^2+26x-1080=0

Solution for 2x^2+26x-1080=0 equation:

Simplifying
2x2 + 26x + -1080 = 0

Reorder the terms:
-1080 + 26x + 2x2 = 0

Solving
-1080 + 26x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-540 + 13x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-540 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
-540 + 13x + x2 = 0

Solving
-540 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '540' to each side of the equation.
-540 + 13x + 540 + x2 = 0 + 540

Reorder the terms:
-540 + 540 + 13x + x2 = 0 + 540

Combine like terms: -540 + 540 = 0
0 + 13x + x2 = 0 + 540
13x + x2 = 0 + 540

Combine like terms: 0 + 540 = 540
13x + x2 = 540

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 = 540 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 540 + 42.25

Combine like terms: 540 + 42.25 = 582.25
42.25 + 13x + x2 = 582.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 582.25

Calculate the square root of the right side: 24.129857024

Break this problem into two subproblems by setting 
(x + 6.5) equal to 24.129857024 and -24.129857024.

Subproblem 1
x + 6.5 = 24.129857024

Simplifying
x + 6.5 = 24.129857024

Reorder the terms:
6.5 + x = 24.129857024

Solving
6.5 + x = 24.129857024

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 = 24.129857024 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 24.129857024 + -6.5
x = 24.129857024 + -6.5

Combine like terms: 24.129857024 + -6.5 = 17.629857024
x = 17.629857024

Simplifying
x = 17.629857024

Subproblem 2
x + 6.5 = -24.129857024

Simplifying
x + 6.5 = -24.129857024

Reorder the terms:
6.5 + x = -24.129857024

Solving
6.5 + x = -24.129857024

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 = -24.129857024 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -24.129857024 + -6.5
x = -24.129857024 + -6.5

Combine like terms: -24.129857024 + -6.5 = -30.629857024
x = -30.629857024

Simplifying
x = -30.629857024

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.629857024, -30.629857024}
Solution
x = {17.629857024, -30.629857024}