2x^2-23x-221=0

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Solution for 2x^2-23x-221=0 equation: 


Simplifying
2x2 + -23x + -221 = 0

Reorder the terms:
-221 + -23x + 2x2 = 0

Solving
-221 + -23x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-110.5 + -11.5x + x2 = 0

Move the constant term to the right:

Add '110.5' to each side of the equation.
-110.5 + -11.5x + 110.5 + x2 = 0 + 110.5

Reorder the terms:
-110.5 + 110.5 + -11.5x + x2 = 0 + 110.5

Combine like terms: -110.5 + 110.5 = 0.0
0.0 + -11.5x + x2 = 0 + 110.5
-11.5x + x2 = 0 + 110.5

Combine like terms: 0 + 110.5 = 110.5
-11.5x + x2 = 110.5

The x term is -11.5x.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5x + 33.0625 + x2 = 110.5 + 33.0625

Reorder the terms:
33.0625 + -11.5x + x2 = 110.5 + 33.0625

Combine like terms: 110.5 + 33.0625 = 143.5625
33.0625 + -11.5x + x2 = 143.5625

Factor a perfect square on the left side:
(x + -5.75)(x + -5.75) = 143.5625

Calculate the square root of the right side: 11.981756966

Break this problem into two subproblems by setting 
(x + -5.75) equal to 11.981756966 and -11.981756966.


Subproblem 1
x + -5.75 = 11.981756966

Simplifying
x + -5.75 = 11.981756966

Reorder the terms:
-5.75 + x = 11.981756966

Solving
-5.75 + x = 11.981756966

Solving for variable 'x'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = 11.981756966 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = 11.981756966 + 5.75
x = 11.981756966 + 5.75

Combine like terms: 11.981756966 + 5.75 = 17.731756966
x = 17.731756966

Simplifying
x = 17.731756966


Subproblem 2
x + -5.75 = -11.981756966

Simplifying
x + -5.75 = -11.981756966

Reorder the terms:
-5.75 + x = -11.981756966

Solving
-5.75 + x = -11.981756966

Solving for variable 'x'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = -11.981756966 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = -11.981756966 + 5.75
x = -11.981756966 + 5.75

Combine like terms: -11.981756966 + 5.75 = -6.231756966
x = -6.231756966

Simplifying
x = -6.231756966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.731756966, -6.231756966}

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