9x^2+32x-144=0

Solution for 9x^2+32x-144=0 equation:

Simplifying
9x2 + 32x + -144 = 0

Reorder the terms:
-144 + 32x + 9x2 = 0

Solving
-144 + 32x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-16 + 3.555555556x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3.555555556x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 3.555555556x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3.555555556x + x2 = 0 + 16
3.555555556x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
3.555555556x + x2 = 16

The x term is 3.555555556x.  Take half its coefficient (1.777777778).
Square it (3.160493828) and add it to both sides.

Add '3.160493828' to each side of the equation.
3.555555556x + 3.160493828 + x2 = 16 + 3.160493828

Reorder the terms:
3.160493828 + 3.555555556x + x2 = 16 + 3.160493828

Combine like terms: 16 + 3.160493828 = 19.160493828
3.160493828 + 3.555555556x + x2 = 19.160493828

Factor a perfect square on the left side:
(x + 1.777777778)(x + 1.777777778) = 19.160493828

Calculate the square root of the right side: 4.377270134

Break this problem into two subproblems by setting 
(x + 1.777777778) equal to 4.377270134 and -4.377270134.

Subproblem 1
x + 1.777777778 = 4.377270134

Simplifying
x + 1.777777778 = 4.377270134

Reorder the terms:
1.777777778 + x = 4.377270134

Solving
1.777777778 + x = 4.377270134

Solving for variable 'x'.

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

Add '-1.777777778' to each side of the equation.
1.777777778 + -1.777777778 + x = 4.377270134 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + x = 4.377270134 + -1.777777778
x = 4.377270134 + -1.777777778

Combine like terms: 4.377270134 + -1.777777778 = 2.599492356
x = 2.599492356

Simplifying
x = 2.599492356

Subproblem 2
x + 1.777777778 = -4.377270134

Simplifying
x + 1.777777778 = -4.377270134

Reorder the terms:
1.777777778 + x = -4.377270134

Solving
1.777777778 + x = -4.377270134

Solving for variable 'x'.

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

Add '-1.777777778' to each side of the equation.
1.777777778 + -1.777777778 + x = -4.377270134 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + x = -4.377270134 + -1.777777778
x = -4.377270134 + -1.777777778

Combine like terms: -4.377270134 + -1.777777778 = -6.155047912
x = -6.155047912

Simplifying
x = -6.155047912

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.599492356, -6.155047912}