32x^2-24x-72=0

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Solution for 32x^2-24x-72=0 equation: 


Simplifying
32x2 + -24x + -72 = 0

Reorder the terms:
-72 + -24x + 32x2 = 0

Solving
-72 + -24x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-9 + -3x + 4x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-9 + -3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-9 + -3x + 4x2 = 0

Solving
-9 + -3x + 4x2 = 0

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

Divide each side by '4'.
-2.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.75x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.75x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.75x + x2 = 0 + 2.25
-0.75x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.75x + x2 = 2.25

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 2.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 2.25 + 0.140625

Combine like terms: 2.25 + 0.140625 = 2.390625
0.140625 + -0.75x + x2 = 2.390625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.54616461 and -1.54616461.


Subproblem 1
x + -0.375 = 1.54616461

Simplifying
x + -0.375 = 1.54616461

Reorder the terms:
-0.375 + x = 1.54616461

Solving
-0.375 + x = 1.54616461

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.54616461 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.54616461 + 0.375
x = 1.54616461 + 0.375

Combine like terms: 1.54616461 + 0.375 = 1.92116461
x = 1.92116461

Simplifying
x = 1.92116461


Subproblem 2
x + -0.375 = -1.54616461

Simplifying
x + -0.375 = -1.54616461

Reorder the terms:
-0.375 + x = -1.54616461

Solving
-0.375 + x = -1.54616461

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.54616461 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.54616461 + 0.375
x = -1.54616461 + 0.375

Combine like terms: -1.54616461 + 0.375 = -1.17116461
x = -1.17116461

Simplifying
x = -1.17116461


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.92116461, -1.17116461}
Solution
x = {1.92116461, -1.17116461}

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