-16x^2+80x+100=0

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Solution for -16x^2+80x+100=0 equation: 


Simplifying
-16x2 + 80x + 100 = 0

Reorder the terms:
100 + 80x + -16x2 = 0

Solving
100 + 80x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + 20x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(25 + 20x + -4x2)' equal to zero and attempt to solve:

Simplifying
25 + 20x + -4x2 = 0

Solving
25 + 20x + -4x2 = 0

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

Divide each side by '-4'.
-6.25 + -5x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -5x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -5x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -5x + x2 = 0 + 6.25
-5x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-5x + x2 = 6.25

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 6.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 6.25 + 6.25

Combine like terms: 6.25 + 6.25 = 12.5
6.25 + -5x + x2 = 12.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.535533906 and -3.535533906.


Subproblem 1
x + -2.5 = 3.535533906

Simplifying
x + -2.5 = 3.535533906

Reorder the terms:
-2.5 + x = 3.535533906

Solving
-2.5 + x = 3.535533906

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.535533906 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.535533906 + 2.5
x = 3.535533906 + 2.5

Combine like terms: 3.535533906 + 2.5 = 6.035533906
x = 6.035533906

Simplifying
x = 6.035533906


Subproblem 2
x + -2.5 = -3.535533906

Simplifying
x + -2.5 = -3.535533906

Reorder the terms:
-2.5 + x = -3.535533906

Solving
-2.5 + x = -3.535533906

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.535533906 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.535533906 + 2.5
x = -3.535533906 + 2.5

Combine like terms: -3.535533906 + 2.5 = -1.035533906
x = -1.035533906

Simplifying
x = -1.035533906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.035533906, -1.035533906}
Solution
x = {6.035533906, -1.035533906}

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