-16x^2+96x+12=0

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Solution for -16x^2+96x+12=0 equation: 


Simplifying
-16x2 + 96x + 12 = 0

Reorder the terms:
12 + 96x + -16x2 = 0

Solving
12 + 96x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 24x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 24x + -4x2)' equal to zero and attempt to solve:

Simplifying
3 + 24x + -4x2 = 0

Solving
3 + 24x + -4x2 = 0

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

Divide each side by '-4'.
-0.75 + -6x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -6x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -6x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -6x + x2 = 0 + 0.75
-6x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-6x + x2 = 0.75

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 0.75 + 9

Reorder the terms:
9 + -6x + x2 = 0.75 + 9

Combine like terms: 0.75 + 9 = 9.75
9 + -6x + x2 = 9.75

Factor a perfect square on the left side:
(x + -3)(x + -3) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + -3) equal to 3.122498999 and -3.122498999.


Subproblem 1
x + -3 = 3.122498999

Simplifying
x + -3 = 3.122498999

Reorder the terms:
-3 + x = 3.122498999

Solving
-3 + x = 3.122498999

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.122498999 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.122498999 + 3
x = 3.122498999 + 3

Combine like terms: 3.122498999 + 3 = 6.122498999
x = 6.122498999

Simplifying
x = 6.122498999


Subproblem 2
x + -3 = -3.122498999

Simplifying
x + -3 = -3.122498999

Reorder the terms:
-3 + x = -3.122498999

Solving
-3 + x = -3.122498999

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.122498999 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.122498999 + 3
x = -3.122498999 + 3

Combine like terms: -3.122498999 + 3 = -0.122498999
x = -0.122498999

Simplifying
x = -0.122498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.122498999, -0.122498999}
Solution
x = {6.122498999, -0.122498999}

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