x^2-5x-244=0

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Solution for x^2-5x-244=0 equation: 


Simplifying
x2 + -5x + -244 = 0

Reorder the terms:
-244 + -5x + x2 = 0

Solving
-244 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '244' to each side of the equation.
-244 + -5x + 244 + x2 = 0 + 244

Reorder the terms:
-244 + 244 + -5x + x2 = 0 + 244

Combine like terms: -244 + 244 = 0
0 + -5x + x2 = 0 + 244
-5x + x2 = 0 + 244

Combine like terms: 0 + 244 = 244
-5x + x2 = 244

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 244 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 244 + 6.25

Combine like terms: 244 + 6.25 = 250.25
6.25 + -5x + x2 = 250.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 250.25

Calculate the square root of the right side: 15.81929202

Break this problem into two subproblems by setting 
(x + -2.5) equal to 15.81929202 and -15.81929202.


Subproblem 1
x + -2.5 = 15.81929202

Simplifying
x + -2.5 = 15.81929202

Reorder the terms:
-2.5 + x = 15.81929202

Solving
-2.5 + x = 15.81929202

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 15.81929202 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 15.81929202 + 2.5
x = 15.81929202 + 2.5

Combine like terms: 15.81929202 + 2.5 = 18.31929202
x = 18.31929202

Simplifying
x = 18.31929202


Subproblem 2
x + -2.5 = -15.81929202

Simplifying
x + -2.5 = -15.81929202

Reorder the terms:
-2.5 + x = -15.81929202

Solving
-2.5 + x = -15.81929202

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -15.81929202 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -15.81929202 + 2.5
x = -15.81929202 + 2.5

Combine like terms: -15.81929202 + 2.5 = -13.31929202
x = -13.31929202

Simplifying
x = -13.31929202


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.31929202, -13.31929202}

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