x^2+5x-250=0

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Solution for x^2+5x-250=0 equation: 


Simplifying
x2 + 5x + -250 = 0

Reorder the terms:
-250 + 5x + x2 = 0

Solving
-250 + 5x + 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 + 5x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + 5x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 5x + x2 = 0 + 250
5x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
5x + x2 = 250

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 = 250 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 250 + 6.25

Combine like terms: 250 + 6.25 = 256.25
6.25 + 5x + x2 = 256.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 256.25

Calculate the square root of the right side: 16.007810594

Break this problem into two subproblems by setting 
(x + 2.5) equal to 16.007810594 and -16.007810594.


Subproblem 1
x + 2.5 = 16.007810594

Simplifying
x + 2.5 = 16.007810594

Reorder the terms:
2.5 + x = 16.007810594

Solving
2.5 + x = 16.007810594

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 = 16.007810594 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 16.007810594 + -2.5
x = 16.007810594 + -2.5

Combine like terms: 16.007810594 + -2.5 = 13.507810594
x = 13.507810594

Simplifying
x = 13.507810594


Subproblem 2
x + 2.5 = -16.007810594

Simplifying
x + 2.5 = -16.007810594

Reorder the terms:
2.5 + x = -16.007810594

Solving
2.5 + x = -16.007810594

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 = -16.007810594 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -16.007810594 + -2.5
x = -16.007810594 + -2.5

Combine like terms: -16.007810594 + -2.5 = -18.507810594
x = -18.507810594

Simplifying
x = -18.507810594


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.507810594, -18.507810594}

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