2x^2-20x-4=0

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


Simplifying
2x2 + -20x + -4 = 0

Reorder the terms:
-4 + -20x + 2x2 = 0

Solving
-4 + -20x + 2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -10x + x2 = 0

Solving
-2 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -10x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -10x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -10x + x2 = 0 + 2
-10x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-10x + x2 = 2

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 = 2 + 25

Reorder the terms:
25 + -10x + x2 = 2 + 25

Combine like terms: 2 + 25 = 27
25 + -10x + x2 = 27

Factor a perfect square on the left side:
(x + -5)(x + -5) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -5) equal to 5.196152423 and -5.196152423.


Subproblem 1
x + -5 = 5.196152423

Simplifying
x + -5 = 5.196152423

Reorder the terms:
-5 + x = 5.196152423

Solving
-5 + x = 5.196152423

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 = 5.196152423 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.196152423 + 5
x = 5.196152423 + 5

Combine like terms: 5.196152423 + 5 = 10.196152423
x = 10.196152423

Simplifying
x = 10.196152423


Subproblem 2
x + -5 = -5.196152423

Simplifying
x + -5 = -5.196152423

Reorder the terms:
-5 + x = -5.196152423

Solving
-5 + x = -5.196152423

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 = -5.196152423 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.196152423 + 5
x = -5.196152423 + 5

Combine like terms: -5.196152423 + 5 = -0.196152423
x = -0.196152423

Simplifying
x = -0.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.196152423, -0.196152423}
Solution
x = {10.196152423, -0.196152423}

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