-16x^2-12x+256=0

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Solution for -16x^2-12x+256=0 equation: 


Simplifying
-16x2 + -12x + 256 = 0

Reorder the terms:
256 + -12x + -16x2 = 0

Solving
256 + -12x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(64 + -3x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(64 + -3x + -4x2)' equal to zero and attempt to solve:

Simplifying
64 + -3x + -4x2 = 0

Solving
64 + -3x + -4x2 = 0

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

Divide each side by '-4'.
-16 + 0.75x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.75x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.75x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.75x + x2 = 0 + 16
0.75x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.75x + x2 = 16

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 = 16 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 16 + 0.140625

Combine like terms: 16 + 0.140625 = 16.140625
0.140625 + 0.75x + x2 = 16.140625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 16.140625

Calculate the square root of the right side: 4.01753967

Break this problem into two subproblems by setting 
(x + 0.375) equal to 4.01753967 and -4.01753967.


Subproblem 1
x + 0.375 = 4.01753967

Simplifying
x + 0.375 = 4.01753967

Reorder the terms:
0.375 + x = 4.01753967

Solving
0.375 + x = 4.01753967

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 = 4.01753967 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 4.01753967 + -0.375
x = 4.01753967 + -0.375

Combine like terms: 4.01753967 + -0.375 = 3.64253967
x = 3.64253967

Simplifying
x = 3.64253967


Subproblem 2
x + 0.375 = -4.01753967

Simplifying
x + 0.375 = -4.01753967

Reorder the terms:
0.375 + x = -4.01753967

Solving
0.375 + x = -4.01753967

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 = -4.01753967 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -4.01753967 + -0.375
x = -4.01753967 + -0.375

Combine like terms: -4.01753967 + -0.375 = -4.39253967
x = -4.39253967

Simplifying
x = -4.39253967


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.64253967, -4.39253967}
Solution
x = {3.64253967, -4.39253967}

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