4x^2+72x-640=0

Solution for 4x^2+72x-640=0 equation:

Simplifying
4x2 + 72x + -640 = 0

Reorder the terms:
-640 + 72x + 4x2 = 0

Solving
-640 + 72x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-160 + 18x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-160 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
-160 + 18x + x2 = 0

Solving
-160 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 18x + 160 + x2 = 0 + 160

Reorder the terms:
-160 + 160 + 18x + x2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + 18x + x2 = 0 + 160
18x + x2 = 0 + 160

Combine like terms: 0 + 160 = 160
18x + x2 = 160

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 160 + 81

Reorder the terms:
81 + 18x + x2 = 160 + 81

Combine like terms: 160 + 81 = 241
81 + 18x + x2 = 241

Factor a perfect square on the left side:
(x + 9)(x + 9) = 241

Calculate the square root of the right side: 15.524174696

Break this problem into two subproblems by setting 
(x + 9) equal to 15.524174696 and -15.524174696.

Subproblem 1
x + 9 = 15.524174696

Simplifying
x + 9 = 15.524174696

Reorder the terms:
9 + x = 15.524174696

Solving
9 + x = 15.524174696

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 15.524174696 + -9

Combine like terms: 9 + -9 = 0
0 + x = 15.524174696 + -9
x = 15.524174696 + -9

Combine like terms: 15.524174696 + -9 = 6.524174696
x = 6.524174696

Simplifying
x = 6.524174696

Subproblem 2
x + 9 = -15.524174696

Simplifying
x + 9 = -15.524174696

Reorder the terms:
9 + x = -15.524174696

Solving
9 + x = -15.524174696

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -15.524174696 + -9

Combine like terms: 9 + -9 = 0
0 + x = -15.524174696 + -9
x = -15.524174696 + -9

Combine like terms: -15.524174696 + -9 = -24.524174696
x = -24.524174696

Simplifying
x = -24.524174696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.524174696, -24.524174696}
Solution
x = {6.524174696, -24.524174696}