32x^2-24x-2=0

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


Simplifying
32x2 + -24x + -2 = 0

Reorder the terms:
-2 + -24x + 32x2 = 0

Solving
-2 + -24x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -12x + 16x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -12x + 16x2)' equal to zero and attempt to solve:

Simplifying
-1 + -12x + 16x2 = 0

Solving
-1 + -12x + 16x2 = 0

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

Divide each side by '16'.
-0.0625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + -0.75x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + -0.75x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + -0.75x + x2 = 0 + 0.0625
-0.75x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
-0.75x + x2 = 0.0625

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 = 0.0625 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.0625 + 0.140625

Combine like terms: 0.0625 + 0.140625 = 0.203125
0.140625 + -0.75x + x2 = 0.203125

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.203125

Calculate the square root of the right side: 0.450693909

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.450693909 and -0.450693909.


Subproblem 1
x + -0.375 = 0.450693909

Simplifying
x + -0.375 = 0.450693909

Reorder the terms:
-0.375 + x = 0.450693909

Solving
-0.375 + x = 0.450693909

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 = 0.450693909 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 0.450693909 + 0.375
x = 0.450693909 + 0.375

Combine like terms: 0.450693909 + 0.375 = 0.825693909
x = 0.825693909

Simplifying
x = 0.825693909


Subproblem 2
x + -0.375 = -0.450693909

Simplifying
x + -0.375 = -0.450693909

Reorder the terms:
-0.375 + x = -0.450693909

Solving
-0.375 + x = -0.450693909

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 = -0.450693909 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -0.450693909 + 0.375
x = -0.450693909 + 0.375

Combine like terms: -0.450693909 + 0.375 = -0.075693909
x = -0.075693909

Simplifying
x = -0.075693909


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.825693909, -0.075693909}
Solution
x = {0.825693909, -0.075693909}

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