-20x^2-250x+1500=0

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Solution for -20x^2-250x+1500=0 equation: 


Simplifying
-20x2 + -250x + 1500 = 0

Reorder the terms:
1500 + -250x + -20x2 = 0

Solving
1500 + -250x + -20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(150 + -25x + -2x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(150 + -25x + -2x2)' equal to zero and attempt to solve:

Simplifying
150 + -25x + -2x2 = 0

Solving
150 + -25x + -2x2 = 0

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

Divide each side by '-2'.
-75 + 12.5x + x2 = 0

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 12.5x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 12.5x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 12.5x + x2 = 0 + 75
12.5x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
12.5x + x2 = 75

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 = 75 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = 75 + 39.0625

Combine like terms: 75 + 39.0625 = 114.0625
39.0625 + 12.5x + x2 = 114.0625

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 114.0625

Calculate the square root of the right side: 10.680004682

Break this problem into two subproblems by setting 
(x + 6.25) equal to 10.680004682 and -10.680004682.


Subproblem 1
x + 6.25 = 10.680004682

Simplifying
x + 6.25 = 10.680004682

Reorder the terms:
6.25 + x = 10.680004682

Solving
6.25 + x = 10.680004682

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 = 10.680004682 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 10.680004682 + -6.25
x = 10.680004682 + -6.25

Combine like terms: 10.680004682 + -6.25 = 4.430004682
x = 4.430004682

Simplifying
x = 4.430004682


Subproblem 2
x + 6.25 = -10.680004682

Simplifying
x + 6.25 = -10.680004682

Reorder the terms:
6.25 + x = -10.680004682

Solving
6.25 + x = -10.680004682

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 = -10.680004682 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -10.680004682 + -6.25
x = -10.680004682 + -6.25

Combine like terms: -10.680004682 + -6.25 = -16.930004682
x = -16.930004682

Simplifying
x = -16.930004682


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.430004682, -16.930004682}
Solution
x = {4.430004682, -16.930004682}

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