x^2+x-252=

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

Simplifying
x2 + x + -252 = 0

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

Solving
-252 + x + 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 + x + 252 + x2 = 0 + 252

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 252 + 0.25

Reorder the terms:
0.25 + x + x2 = 252 + 0.25

Combine like terms: 252 + 0.25 = 252.25
0.25 + x + x2 = 252.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 252.25

Calculate the square root of the right side: 15.882380174

Break this problem into two subproblems by setting 
(x + 0.5) equal to 15.882380174 and -15.882380174.

Subproblem 1
x + 0.5 = 15.882380174

Simplifying
x + 0.5 = 15.882380174

Reorder the terms:
0.5 + x = 15.882380174

Solving
0.5 + x = 15.882380174

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 15.882380174 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 15.882380174 + -0.5
x = 15.882380174 + -0.5

Combine like terms: 15.882380174 + -0.5 = 15.382380174
x = 15.382380174

Simplifying
x = 15.382380174

Subproblem 2
x + 0.5 = -15.882380174

Simplifying
x + 0.5 = -15.882380174

Reorder the terms:
0.5 + x = -15.882380174

Solving
0.5 + x = -15.882380174

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -15.882380174 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -15.882380174 + -0.5
x = -15.882380174 + -0.5

Combine like terms: -15.882380174 + -0.5 = -16.382380174
x = -16.382380174

Simplifying
x = -16.382380174

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.382380174, -16.382380174}