4x^2-40x-20=0

Solution for 4x^2-40x-20=0 equation:

Simplifying
4x2 + -40x + -20 = 0

Reorder the terms:
-20 + -40x + 4x2 = 0

Solving
-20 + -40x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -10x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + -10x + x2 = 0

Solving
-5 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -10x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -10x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -10x + x2 = 0 + 5
-10x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-10x + x2 = 5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 5 + 25

Reorder the terms:
25 + -10x + x2 = 5 + 25

Combine like terms: 5 + 25 = 30
25 + -10x + x2 = 30

Factor a perfect square on the left side:
(x + -5)(x + -5) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + -5) equal to 5.477225575 and -5.477225575.

Subproblem 1
x + -5 = 5.477225575

Simplifying
x + -5 = 5.477225575

Reorder the terms:
-5 + x = 5.477225575

Solving
-5 + x = 5.477225575

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.477225575 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.477225575 + 5
x = 5.477225575 + 5

Combine like terms: 5.477225575 + 5 = 10.477225575
x = 10.477225575

Simplifying
x = 10.477225575

Subproblem 2
x + -5 = -5.477225575

Simplifying
x + -5 = -5.477225575

Reorder the terms:
-5 + x = -5.477225575

Solving
-5 + x = -5.477225575

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.477225575 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.477225575 + 5
x = -5.477225575 + 5

Combine like terms: -5.477225575 + 5 = -0.477225575
x = -0.477225575

Simplifying
x = -0.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.477225575, -0.477225575}
Solution
x = {10.477225575, -0.477225575}