2x^2+13x-40=0

Solution for 2x^2+13x-40=0 equation:

Simplifying
2x2 + 13x + -40 = 0

Reorder the terms:
-40 + 13x + 2x2 = 0

Solving
-40 + 13x + 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'.
-20 + 6.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 6.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 6.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 6.5x + x2 = 0 + 20
6.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
6.5x + x2 = 20

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 20 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 20 + 10.5625

Combine like terms: 20 + 10.5625 = 30.5625
10.5625 + 6.5x + x2 = 30.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 30.5625

Calculate the square root of the right side: 5.528336097

Break this problem into two subproblems by setting 
(x + 3.25) equal to 5.528336097 and -5.528336097.

Subproblem 1
x + 3.25 = 5.528336097

Simplifying
x + 3.25 = 5.528336097

Reorder the terms:
3.25 + x = 5.528336097

Solving
3.25 + x = 5.528336097

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 5.528336097 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 5.528336097 + -3.25
x = 5.528336097 + -3.25

Combine like terms: 5.528336097 + -3.25 = 2.278336097
x = 2.278336097

Simplifying
x = 2.278336097

Subproblem 2
x + 3.25 = -5.528336097

Simplifying
x + 3.25 = -5.528336097

Reorder the terms:
3.25 + x = -5.528336097

Solving
3.25 + x = -5.528336097

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -5.528336097 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -5.528336097 + -3.25
x = -5.528336097 + -3.25

Combine like terms: -5.528336097 + -3.25 = -8.778336097
x = -8.778336097

Simplifying
x = -8.778336097

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.278336097, -8.778336097}