2x^2+24x-160=0

Solution for 2x^2+24x-160=0 equation:

Simplifying
2x2 + 24x + -160 = 0

Reorder the terms:
-160 + 24x + 2x2 = 0

Solving
-160 + 24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-80 + 12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-80 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-80 + 12x + x2 = 0

Solving
-80 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 12x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + 12x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 12x + x2 = 0 + 80
12x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
12x + x2 = 80

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 80 + 36

Reorder the terms:
36 + 12x + x2 = 80 + 36

Combine like terms: 80 + 36 = 116
36 + 12x + x2 = 116

Factor a perfect square on the left side:
(x + 6)(x + 6) = 116

Calculate the square root of the right side: 10.770329614

Break this problem into two subproblems by setting 
(x + 6) equal to 10.770329614 and -10.770329614.

Subproblem 1
x + 6 = 10.770329614

Simplifying
x + 6 = 10.770329614

Reorder the terms:
6 + x = 10.770329614

Solving
6 + x = 10.770329614

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 10.770329614 + -6

Combine like terms: 6 + -6 = 0
0 + x = 10.770329614 + -6
x = 10.770329614 + -6

Combine like terms: 10.770329614 + -6 = 4.770329614
x = 4.770329614

Simplifying
x = 4.770329614

Subproblem 2
x + 6 = -10.770329614

Simplifying
x + 6 = -10.770329614

Reorder the terms:
6 + x = -10.770329614

Solving
6 + x = -10.770329614

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -10.770329614 + -6

Combine like terms: 6 + -6 = 0
0 + x = -10.770329614 + -6
x = -10.770329614 + -6

Combine like terms: -10.770329614 + -6 = -16.770329614
x = -16.770329614

Simplifying
x = -16.770329614

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.770329614, -16.770329614}
Solution
x = {4.770329614, -16.770329614}