20x^2-60x-500=0

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Solution for 20x^2-60x-500=0 equation: 


Simplifying
20x2 + -60x + -500 = 0

Reorder the terms:
-500 + -60x + 20x2 = 0

Solving
-500 + -60x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-25 + -3x + x2) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(-25 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-25 + -3x + x2 = 0

Solving
-25 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -3x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -3x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -3x + x2 = 0 + 25
-3x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-3x + x2 = 25

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 25 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 25 + 2.25

Combine like terms: 25 + 2.25 = 27.25
2.25 + -3x + x2 = 27.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.220153254 and -5.220153254.


Subproblem 1
x + -1.5 = 5.220153254

Simplifying
x + -1.5 = 5.220153254

Reorder the terms:
-1.5 + x = 5.220153254

Solving
-1.5 + x = 5.220153254

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 5.220153254 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 5.220153254 + 1.5
x = 5.220153254 + 1.5

Combine like terms: 5.220153254 + 1.5 = 6.720153254
x = 6.720153254

Simplifying
x = 6.720153254


Subproblem 2
x + -1.5 = -5.220153254

Simplifying
x + -1.5 = -5.220153254

Reorder the terms:
-1.5 + x = -5.220153254

Solving
-1.5 + x = -5.220153254

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -5.220153254 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -5.220153254 + 1.5
x = -5.220153254 + 1.5

Combine like terms: -5.220153254 + 1.5 = -3.720153254
x = -3.720153254

Simplifying
x = -3.720153254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.720153254, -3.720153254}
Solution
x = {6.720153254, -3.720153254}

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