4x^2+10x-32=0

Solution for 4x^2+10x-32=0 equation:

Simplifying
4x2 + 10x + -32 = 0

Reorder the terms:
-32 + 10x + 4x2 = 0

Solving
-32 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 5x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-16 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-16 + 5x + 2x2 = 0

Solving
-16 + 5x + 2x2 = 0

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

Divide each side by '2'.
-8 + 2.5x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 2.5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 2.5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2.5x + x2 = 0 + 8
2.5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
2.5x + x2 = 8

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 8 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 8 + 1.5625

Combine like terms: 8 + 1.5625 = 9.5625
1.5625 + 2.5x + x2 = 9.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.092329219 and -3.092329219.

Subproblem 1
x + 1.25 = 3.092329219

Simplifying
x + 1.25 = 3.092329219

Reorder the terms:
1.25 + x = 3.092329219

Solving
1.25 + x = 3.092329219

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 3.092329219 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 3.092329219 + -1.25
x = 3.092329219 + -1.25

Combine like terms: 3.092329219 + -1.25 = 1.842329219
x = 1.842329219

Simplifying
x = 1.842329219

Subproblem 2
x + 1.25 = -3.092329219

Simplifying
x + 1.25 = -3.092329219

Reorder the terms:
1.25 + x = -3.092329219

Solving
1.25 + x = -3.092329219

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -3.092329219 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -3.092329219 + -1.25
x = -3.092329219 + -1.25

Combine like terms: -3.092329219 + -1.25 = -4.342329219
x = -4.342329219

Simplifying
x = -4.342329219

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.842329219, -4.342329219}
Solution
x = {1.842329219, -4.342329219}