-16x^2+80x+3200=0

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Solution for -16x^2+80x+3200=0 equation:


Simplifying
-16x2 + 80x + 3200 = 0

Reorder the terms:
3200 + 80x + -16x2 = 0

Solving
3200 + 80x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(200 + 5x + -1x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(200 + 5x + -1x2)' equal to zero and attempt to solve:

Simplifying
200 + 5x + -1x2 = 0

Solving
200 + 5x + -1x2 = 0

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

Divide each side by '-1'.
-200 + -5x + x2 = 0

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + -5x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + -5x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -5x + x2 = 0 + 200
-5x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
-5x + x2 = 200

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 = 200 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 200 + 6.25

Combine like terms: 200 + 6.25 = 206.25
6.25 + -5x + x2 = 206.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 206.25

Calculate the square root of the right side: 14.361406616

Break this problem into two subproblems by setting 
(x + -2.5) equal to 14.361406616 and -14.361406616.


Subproblem 1
x + -2.5 = 14.361406616

Simplifying
x + -2.5 = 14.361406616

Reorder the terms:
-2.5 + x = 14.361406616

Solving
-2.5 + x = 14.361406616

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 = 14.361406616 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 14.361406616 + 2.5
x = 14.361406616 + 2.5

Combine like terms: 14.361406616 + 2.5 = 16.861406616
x = 16.861406616

Simplifying
x = 16.861406616


Subproblem 2
x + -2.5 = -14.361406616

Simplifying
x + -2.5 = -14.361406616

Reorder the terms:
-2.5 + x = -14.361406616

Solving
-2.5 + x = -14.361406616

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 = -14.361406616 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -14.361406616 + 2.5
x = -14.361406616 + 2.5

Combine like terms: -14.361406616 + 2.5 = -11.861406616
x = -11.861406616

Simplifying
x = -11.861406616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.861406616, -11.861406616}
Solution
x = {16.861406616, -11.861406616}

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