-16x^2-10x+100=0

Solution for -16x^2-10x+100=0 equation:

Simplifying
-16x2 + -10x + 100 = 0

Reorder the terms:
100 + -10x + -16x2 = 0

Solving
100 + -10x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(50 + -5x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(50 + -5x + -8x2)' equal to zero and attempt to solve:

Simplifying
50 + -5x + -8x2 = 0

Solving
50 + -5x + -8x2 = 0

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

Divide each side by '-8'.
-6.25 + 0.625x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 0.625x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 0.625x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 0.625x + x2 = 0 + 6.25
0.625x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
0.625x + x2 = 6.25

The x term is 0.625x.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625x + 0.09765625 + x2 = 6.25 + 0.09765625

Reorder the terms:
0.09765625 + 0.625x + x2 = 6.25 + 0.09765625

Combine like terms: 6.25 + 0.09765625 = 6.34765625
0.09765625 + 0.625x + x2 = 6.34765625

Factor a perfect square on the left side:
(x + 0.3125)(x + 0.3125) = 6.34765625

Calculate the square root of the right side: 2.519455546

Break this problem into two subproblems by setting 
(x + 0.3125) equal to 2.519455546 and -2.519455546.

Subproblem 1
x + 0.3125 = 2.519455546

Simplifying
x + 0.3125 = 2.519455546

Reorder the terms:
0.3125 + x = 2.519455546

Solving
0.3125 + x = 2.519455546

Solving for variable 'x'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + x = 2.519455546 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + x = 2.519455546 + -0.3125
x = 2.519455546 + -0.3125

Combine like terms: 2.519455546 + -0.3125 = 2.206955546
x = 2.206955546

Simplifying
x = 2.206955546

Subproblem 2
x + 0.3125 = -2.519455546

Simplifying
x + 0.3125 = -2.519455546

Reorder the terms:
0.3125 + x = -2.519455546

Solving
0.3125 + x = -2.519455546

Solving for variable 'x'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + x = -2.519455546 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + x = -2.519455546 + -0.3125
x = -2.519455546 + -0.3125

Combine like terms: -2.519455546 + -0.3125 = -2.831955546
x = -2.831955546

Simplifying
x = -2.831955546

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.206955546, -2.831955546}
Solution
x = {2.206955546, -2.831955546}