-16x^2-30x+100=0

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Solution for -16x^2-30x+100=0 equation: 


Simplifying
-16x2 + -30x + 100 = 0

Reorder the terms:
100 + -30x + -16x2 = 0

Solving
100 + -30x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(50 + -15x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(50 + -15x + -8x2)' equal to zero and attempt to solve:

Simplifying
50 + -15x + -8x2 = 0

Solving
50 + -15x + -8x2 = 0

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

Divide each side by '-8'.
-6.25 + 1.875x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 1.875x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 1.875x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 1.875x + x2 = 0 + 6.25
1.875x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
1.875x + x2 = 6.25

The x term is 1.875x.  Take half its coefficient (0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
1.875x + 0.87890625 + x2 = 6.25 + 0.87890625

Reorder the terms:
0.87890625 + 1.875x + x2 = 6.25 + 0.87890625

Combine like terms: 6.25 + 0.87890625 = 7.12890625
0.87890625 + 1.875x + x2 = 7.12890625

Factor a perfect square on the left side:
(x + 0.9375)(x + 0.9375) = 7.12890625

Calculate the square root of the right side: 2.67000117

Break this problem into two subproblems by setting 
(x + 0.9375) equal to 2.67000117 and -2.67000117.


Subproblem 1
x + 0.9375 = 2.67000117

Simplifying
x + 0.9375 = 2.67000117

Reorder the terms:
0.9375 + x = 2.67000117

Solving
0.9375 + x = 2.67000117

Solving for variable 'x'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + x = 2.67000117 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + x = 2.67000117 + -0.9375
x = 2.67000117 + -0.9375

Combine like terms: 2.67000117 + -0.9375 = 1.73250117
x = 1.73250117

Simplifying
x = 1.73250117


Subproblem 2
x + 0.9375 = -2.67000117

Simplifying
x + 0.9375 = -2.67000117

Reorder the terms:
0.9375 + x = -2.67000117

Solving
0.9375 + x = -2.67000117

Solving for variable 'x'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + x = -2.67000117 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + x = -2.67000117 + -0.9375
x = -2.67000117 + -0.9375

Combine like terms: -2.67000117 + -0.9375 = -3.60750117
x = -3.60750117

Simplifying
x = -3.60750117


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.73250117, -3.60750117}
Solution
x = {1.73250117, -3.60750117}

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