-80x^2-1000x+5000=0

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Solution for -80x^2-1000x+5000=0 equation: 


Simplifying
-80x2 + -1000x + 5000 = 0

Reorder the terms:
5000 + -1000x + -80x2 = 0

Solving
5000 + -1000x + -80x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '40'.
40(125 + -25x + -2x2) = 0

Ignore the factor 40.

Subproblem 1
Set the factor '(125 + -25x + -2x2)' equal to zero and attempt to solve:

Simplifying
125 + -25x + -2x2 = 0

Solving
125 + -25x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-62.5 + 12.5x + x2 = 0

Move the constant term to the right:

Add '62.5' to each side of the equation.
-62.5 + 12.5x + 62.5 + x2 = 0 + 62.5

Reorder the terms:
-62.5 + 62.5 + 12.5x + x2 = 0 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + 12.5x + x2 = 0 + 62.5
12.5x + x2 = 0 + 62.5

Combine like terms: 0 + 62.5 = 62.5
12.5x + x2 = 62.5

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = 62.5 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = 62.5 + 39.0625

Combine like terms: 62.5 + 39.0625 = 101.5625
39.0625 + 12.5x + x2 = 101.5625

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 101.5625

Calculate the square root of the right side: 10.077822185

Break this problem into two subproblems by setting 
(x + 6.25) equal to 10.077822185 and -10.077822185.


Subproblem 1
x + 6.25 = 10.077822185

Simplifying
x + 6.25 = 10.077822185

Reorder the terms:
6.25 + x = 10.077822185

Solving
6.25 + x = 10.077822185

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = 10.077822185 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 10.077822185 + -6.25
x = 10.077822185 + -6.25

Combine like terms: 10.077822185 + -6.25 = 3.827822185
x = 3.827822185

Simplifying
x = 3.827822185


Subproblem 2
x + 6.25 = -10.077822185

Simplifying
x + 6.25 = -10.077822185

Reorder the terms:
6.25 + x = -10.077822185

Solving
6.25 + x = -10.077822185

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = -10.077822185 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -10.077822185 + -6.25
x = -10.077822185 + -6.25

Combine like terms: -10.077822185 + -6.25 = -16.327822185
x = -16.327822185

Simplifying
x = -16.327822185


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.827822185, -16.327822185}
Solution
x = {3.827822185, -16.327822185}

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