5x^2+32x-23=0

Solution for 5x^2+32x-23=0 equation:

Simplifying
5x2 + 32x + -23 = 0

Reorder the terms:
-23 + 32x + 5x2 = 0

Solving
-23 + 32x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-4.6 + 6.4x + x2 = 0

Move the constant term to the right:

Add '4.6' to each side of the equation.
-4.6 + 6.4x + 4.6 + x2 = 0 + 4.6

Reorder the terms:
-4.6 + 4.6 + 6.4x + x2 = 0 + 4.6

Combine like terms: -4.6 + 4.6 = 0.0
0.0 + 6.4x + x2 = 0 + 4.6
6.4x + x2 = 0 + 4.6

Combine like terms: 0 + 4.6 = 4.6
6.4x + x2 = 4.6

The x term is 6.4x.  Take half its coefficient (3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
6.4x + 10.24 + x2 = 4.6 + 10.24

Reorder the terms:
10.24 + 6.4x + x2 = 4.6 + 10.24

Combine like terms: 4.6 + 10.24 = 14.84
10.24 + 6.4x + x2 = 14.84

Factor a perfect square on the left side:
(x + 3.2)(x + 3.2) = 14.84

Calculate the square root of the right side: 3.852272057

Break this problem into two subproblems by setting 
(x + 3.2) equal to 3.852272057 and -3.852272057.

Subproblem 1
x + 3.2 = 3.852272057

Simplifying
x + 3.2 = 3.852272057

Reorder the terms:
3.2 + x = 3.852272057

Solving
3.2 + x = 3.852272057

Solving for variable 'x'.

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

Add '-3.2' to each side of the equation.
3.2 + -3.2 + x = 3.852272057 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + x = 3.852272057 + -3.2
x = 3.852272057 + -3.2

Combine like terms: 3.852272057 + -3.2 = 0.652272057
x = 0.652272057

Simplifying
x = 0.652272057

Subproblem 2
x + 3.2 = -3.852272057

Simplifying
x + 3.2 = -3.852272057

Reorder the terms:
3.2 + x = -3.852272057

Solving
3.2 + x = -3.852272057

Solving for variable 'x'.

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

Add '-3.2' to each side of the equation.
3.2 + -3.2 + x = -3.852272057 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + x = -3.852272057 + -3.2
x = -3.852272057 + -3.2

Combine like terms: -3.852272057 + -3.2 = -7.052272057
x = -7.052272057

Simplifying
x = -7.052272057

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.652272057, -7.052272057}