96x^2-48x-153=0

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Solution for 96x^2-48x-153=0 equation:


Simplifying
96x2 + -48x + -153 = 0

Reorder the terms:
-153 + -48x + 96x2 = 0

Solving
-153 + -48x + 96x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-51 + -16x + 32x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-51 + -16x + 32x2)' equal to zero and attempt to solve:

Simplifying
-51 + -16x + 32x2 = 0

Solving
-51 + -16x + 32x2 = 0

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

Divide each side by '32'.
-1.59375 + -0.5x + x2 = 0

Move the constant term to the right:

Add '1.59375' to each side of the equation.
-1.59375 + -0.5x + 1.59375 + x2 = 0 + 1.59375

Reorder the terms:
-1.59375 + 1.59375 + -0.5x + x2 = 0 + 1.59375

Combine like terms: -1.59375 + 1.59375 = 0.00000
0.00000 + -0.5x + x2 = 0 + 1.59375
-0.5x + x2 = 0 + 1.59375

Combine like terms: 0 + 1.59375 = 1.59375
-0.5x + x2 = 1.59375

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 1.59375 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 1.59375 + 0.0625

Combine like terms: 1.59375 + 0.0625 = 1.65625
0.0625 + -0.5x + x2 = 1.65625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 1.65625

Calculate the square root of the right side: 1.286953768

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.286953768 and -1.286953768.


Subproblem 1
x + -0.25 = 1.286953768

Simplifying
x + -0.25 = 1.286953768

Reorder the terms:
-0.25 + x = 1.286953768

Solving
-0.25 + x = 1.286953768

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 1.286953768 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 1.286953768 + 0.25
x = 1.286953768 + 0.25

Combine like terms: 1.286953768 + 0.25 = 1.536953768
x = 1.536953768

Simplifying
x = 1.536953768


Subproblem 2
x + -0.25 = -1.286953768

Simplifying
x + -0.25 = -1.286953768

Reorder the terms:
-0.25 + x = -1.286953768

Solving
-0.25 + x = -1.286953768

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -1.286953768 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -1.286953768 + 0.25
x = -1.286953768 + 0.25

Combine like terms: -1.286953768 + 0.25 = -1.036953768
x = -1.036953768

Simplifying
x = -1.036953768


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.536953768, -1.036953768}
Solution
x = {1.536953768, -1.036953768}

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