2x^2-20x-884=0

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Solution for 2x^2-20x-884=0 equation: 


Simplifying
2x2 + -20x + -884 = 0

Reorder the terms:
-884 + -20x + 2x2 = 0

Solving
-884 + -20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-442 + -10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-442 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-442 + -10x + x2 = 0

Solving
-442 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '442' to each side of the equation.
-442 + -10x + 442 + x2 = 0 + 442

Reorder the terms:
-442 + 442 + -10x + x2 = 0 + 442

Combine like terms: -442 + 442 = 0
0 + -10x + x2 = 0 + 442
-10x + x2 = 0 + 442

Combine like terms: 0 + 442 = 442
-10x + x2 = 442

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 = 442 + 25

Reorder the terms:
25 + -10x + x2 = 442 + 25

Combine like terms: 442 + 25 = 467
25 + -10x + x2 = 467

Factor a perfect square on the left side:
(x + -5)(x + -5) = 467

Calculate the square root of the right side: 21.610182785

Break this problem into two subproblems by setting 
(x + -5) equal to 21.610182785 and -21.610182785.


Subproblem 1
x + -5 = 21.610182785

Simplifying
x + -5 = 21.610182785

Reorder the terms:
-5 + x = 21.610182785

Solving
-5 + x = 21.610182785

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 = 21.610182785 + 5

Combine like terms: -5 + 5 = 0
0 + x = 21.610182785 + 5
x = 21.610182785 + 5

Combine like terms: 21.610182785 + 5 = 26.610182785
x = 26.610182785

Simplifying
x = 26.610182785


Subproblem 2
x + -5 = -21.610182785

Simplifying
x + -5 = -21.610182785

Reorder the terms:
-5 + x = -21.610182785

Solving
-5 + x = -21.610182785

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 = -21.610182785 + 5

Combine like terms: -5 + 5 = 0
0 + x = -21.610182785 + 5
x = -21.610182785 + 5

Combine like terms: -21.610182785 + 5 = -16.610182785
x = -16.610182785

Simplifying
x = -16.610182785


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.610182785, -16.610182785}
Solution
x = {26.610182785, -16.610182785}

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