(-16x^2)+128x+100=0

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Solution for (-16x^2)+128x+100=0 equation: 


Simplifying
(-16x2) + 128x + 100 = 0

Reorder the terms:
100 + 128x + (-16x2) = 0

Solving
100 + 128x + (-16x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + 32x + (-4x2)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(25 + 32x + (-4x2))' equal to zero and attempt to solve:

Simplifying
25 + 32x + (-4x2) = 0

Solving
25 + 32x + (-4x2) = 0

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

Divide each side by '-4'.
-6.25 + -8x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -8x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -8x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -8x + x2 = 0 + 6.25
-8x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-8x + x2 = 6.25

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 6.25 + 16

Reorder the terms:
16 + -8x + x2 = 6.25 + 16

Combine like terms: 6.25 + 16 = 22.25
16 + -8x + x2 = 22.25

Factor a perfect square on the left side:
((x) + -4)((x) + -4) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
((x) + -4) equal to 4.716990566 and -4.716990566.


Subproblem 1
(x) + -4 = 4.716990566

Simplifying
(x) + -4 = 4.716990566
x + -4 = 4.716990566

Reorder the terms:
-4 + x = 4.716990566

Solving
-4 + x = 4.716990566

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.716990566 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.716990566 + 4
x = 4.716990566 + 4

Combine like terms: 4.716990566 + 4 = 8.716990566
x = 8.716990566

Simplifying
x = 8.716990566


Subproblem 2
(x) + -4 = -4.716990566

Simplifying
(x) + -4 = -4.716990566
x + -4 = -4.716990566

Reorder the terms:
-4 + x = -4.716990566

Solving
-4 + x = -4.716990566

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.716990566 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.716990566 + 4
x = -4.716990566 + 4

Combine like terms: -4.716990566 + 4 = -0.716990566
x = -0.716990566

Simplifying
x = -0.716990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.716990566, -0.716990566}
Solution
x = {8.716990566, -0.716990566}

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