x^2-14x-250=0

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Solution for x^2-14x-250=0 equation: 


Simplifying
x2 + -14x + -250 = 0

Reorder the terms:
-250 + -14x + x2 = 0

Solving
-250 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + -14x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + -14x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + -14x + x2 = 0 + 250
-14x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
-14x + x2 = 250

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 250 + 49

Reorder the terms:
49 + -14x + x2 = 250 + 49

Combine like terms: 250 + 49 = 299
49 + -14x + x2 = 299

Factor a perfect square on the left side:
(x + -7)(x + -7) = 299

Calculate the square root of the right side: 17.291616466

Break this problem into two subproblems by setting 
(x + -7) equal to 17.291616466 and -17.291616466.


Subproblem 1
x + -7 = 17.291616466

Simplifying
x + -7 = 17.291616466

Reorder the terms:
-7 + x = 17.291616466

Solving
-7 + x = 17.291616466

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 17.291616466 + 7

Combine like terms: -7 + 7 = 0
0 + x = 17.291616466 + 7
x = 17.291616466 + 7

Combine like terms: 17.291616466 + 7 = 24.291616466
x = 24.291616466

Simplifying
x = 24.291616466


Subproblem 2
x + -7 = -17.291616466

Simplifying
x + -7 = -17.291616466

Reorder the terms:
-7 + x = -17.291616466

Solving
-7 + x = -17.291616466

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -17.291616466 + 7

Combine like terms: -7 + 7 = 0
0 + x = -17.291616466 + 7
x = -17.291616466 + 7

Combine like terms: -17.291616466 + 7 = -10.291616466
x = -10.291616466

Simplifying
x = -10.291616466


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.291616466, -10.291616466}

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