-16x^2+64x+192=6

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Solution for -16x^2+64x+192=6 equation: 


Simplifying
-16x2 + 64x + 192 = 6

Reorder the terms:
192 + 64x + -16x2 = 6

Solving
192 + 64x + -16x2 = 6

Solving for variable 'x'.

Reorder the terms:
192 + -6 + 64x + -16x2 = 6 + -6

Combine like terms: 192 + -6 = 186
186 + 64x + -16x2 = 6 + -6

Combine like terms: 6 + -6 = 0
186 + 64x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(93 + 32x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(93 + 32x + -8x2)' equal to zero and attempt to solve:

Simplifying
93 + 32x + -8x2 = 0

Solving
93 + 32x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-11.625 + -4x + x2 = 0

Move the constant term to the right:

Add '11.625' to each side of the equation.
-11.625 + -4x + 11.625 + x2 = 0 + 11.625

Reorder the terms:
-11.625 + 11.625 + -4x + x2 = 0 + 11.625

Combine like terms: -11.625 + 11.625 = 0.000
0.000 + -4x + x2 = 0 + 11.625
-4x + x2 = 0 + 11.625

Combine like terms: 0 + 11.625 = 11.625
-4x + x2 = 11.625

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 11.625 + 4

Reorder the terms:
4 + -4x + x2 = 11.625 + 4

Combine like terms: 11.625 + 4 = 15.625
4 + -4x + x2 = 15.625

Factor a perfect square on the left side:
(x + -2)(x + -2) = 15.625

Calculate the square root of the right side: 3.952847075

Break this problem into two subproblems by setting 
(x + -2) equal to 3.952847075 and -3.952847075.


Subproblem 1
x + -2 = 3.952847075

Simplifying
x + -2 = 3.952847075

Reorder the terms:
-2 + x = 3.952847075

Solving
-2 + x = 3.952847075

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 3.952847075 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.952847075 + 2
x = 3.952847075 + 2

Combine like terms: 3.952847075 + 2 = 5.952847075
x = 5.952847075

Simplifying
x = 5.952847075


Subproblem 2
x + -2 = -3.952847075

Simplifying
x + -2 = -3.952847075

Reorder the terms:
-2 + x = -3.952847075

Solving
-2 + x = -3.952847075

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -3.952847075 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.952847075 + 2
x = -3.952847075 + 2

Combine like terms: -3.952847075 + 2 = -1.952847075
x = -1.952847075

Simplifying
x = -1.952847075


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.952847075, -1.952847075}
Solution
x = {5.952847075, -1.952847075}

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