-16x^2+96x+800=0

Solution for -16x^2+96x+800=0 equation:

Simplifying
-16x2 + 96x + 800 = 0

Reorder the terms:
800 + 96x + -16x2 = 0

Solving
800 + 96x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(50 + 6x + -1x2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(50 + 6x + -1x2)' equal to zero and attempt to solve:

Simplifying
50 + 6x + -1x2 = 0

Solving
50 + 6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-50 + -6x + x2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -6x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -6x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -6x + x2 = 0 + 50
-6x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-6x + x2 = 50

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 50 + 9

Reorder the terms:
9 + -6x + x2 = 50 + 9

Combine like terms: 50 + 9 = 59
9 + -6x + x2 = 59

Factor a perfect square on the left side:
(x + -3)(x + -3) = 59

Calculate the square root of the right side: 7.681145748

Break this problem into two subproblems by setting 
(x + -3) equal to 7.681145748 and -7.681145748.

Subproblem 1
x + -3 = 7.681145748

Simplifying
x + -3 = 7.681145748

Reorder the terms:
-3 + x = 7.681145748

Solving
-3 + x = 7.681145748

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 7.681145748 + 3

Combine like terms: -3 + 3 = 0
0 + x = 7.681145748 + 3
x = 7.681145748 + 3

Combine like terms: 7.681145748 + 3 = 10.681145748
x = 10.681145748

Simplifying
x = 10.681145748

Subproblem 2
x + -3 = -7.681145748

Simplifying
x + -3 = -7.681145748

Reorder the terms:
-3 + x = -7.681145748

Solving
-3 + x = -7.681145748

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -7.681145748 + 3

Combine like terms: -3 + 3 = 0
0 + x = -7.681145748 + 3
x = -7.681145748 + 3

Combine like terms: -7.681145748 + 3 = -4.681145748
x = -4.681145748

Simplifying
x = -4.681145748

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.681145748, -4.681145748}
Solution
x = {10.681145748, -4.681145748}