x^2+10x-252=0

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Solution for x^2+10x-252=0 equation: 


Simplifying
x2 + 10x + -252 = 0

Reorder the terms:
-252 + 10x + x2 = 0

Solving
-252 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '252' to each side of the equation.
-252 + 10x + 252 + x2 = 0 + 252

Reorder the terms:
-252 + 252 + 10x + x2 = 0 + 252

Combine like terms: -252 + 252 = 0
0 + 10x + x2 = 0 + 252
10x + x2 = 0 + 252

Combine like terms: 0 + 252 = 252
10x + x2 = 252

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 = 252 + 25

Reorder the terms:
25 + 10x + x2 = 252 + 25

Combine like terms: 252 + 25 = 277
25 + 10x + x2 = 277

Factor a perfect square on the left side:
(x + 5)(x + 5) = 277

Calculate the square root of the right side: 16.643316977

Break this problem into two subproblems by setting 
(x + 5) equal to 16.643316977 and -16.643316977.


Subproblem 1
x + 5 = 16.643316977

Simplifying
x + 5 = 16.643316977

Reorder the terms:
5 + x = 16.643316977

Solving
5 + x = 16.643316977

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 = 16.643316977 + -5

Combine like terms: 5 + -5 = 0
0 + x = 16.643316977 + -5
x = 16.643316977 + -5

Combine like terms: 16.643316977 + -5 = 11.643316977
x = 11.643316977

Simplifying
x = 11.643316977


Subproblem 2
x + 5 = -16.643316977

Simplifying
x + 5 = -16.643316977

Reorder the terms:
5 + x = -16.643316977

Solving
5 + x = -16.643316977

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 = -16.643316977 + -5

Combine like terms: 5 + -5 = 0
0 + x = -16.643316977 + -5
x = -16.643316977 + -5

Combine like terms: -16.643316977 + -5 = -21.643316977
x = -21.643316977

Simplifying
x = -21.643316977


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.643316977, -21.643316977}

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