x^2+x-315=0

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Solution for x^2+x-315=0 equation: 


Simplifying
x2 + x + -315 = 0

Reorder the terms:
-315 + x + x2 = 0

Solving
-315 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '315' to each side of the equation.
-315 + x + 315 + x2 = 0 + 315

Reorder the terms:
-315 + 315 + x + x2 = 0 + 315

Combine like terms: -315 + 315 = 0
0 + x + x2 = 0 + 315
x + x2 = 0 + 315

Combine like terms: 0 + 315 = 315
x + x2 = 315

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 = 315 + 0.25

Reorder the terms:
0.25 + x + x2 = 315 + 0.25

Combine like terms: 315 + 0.25 = 315.25
0.25 + x + x2 = 315.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 315.25

Calculate the square root of the right side: 17.755280905

Break this problem into two subproblems by setting 
(x + 0.5) equal to 17.755280905 and -17.755280905.


Subproblem 1
x + 0.5 = 17.755280905

Simplifying
x + 0.5 = 17.755280905

Reorder the terms:
0.5 + x = 17.755280905

Solving
0.5 + x = 17.755280905

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 = 17.755280905 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 17.755280905 + -0.5
x = 17.755280905 + -0.5

Combine like terms: 17.755280905 + -0.5 = 17.255280905
x = 17.255280905

Simplifying
x = 17.255280905


Subproblem 2
x + 0.5 = -17.755280905

Simplifying
x + 0.5 = -17.755280905

Reorder the terms:
0.5 + x = -17.755280905

Solving
0.5 + x = -17.755280905

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 = -17.755280905 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -17.755280905 + -0.5
x = -17.755280905 + -0.5

Combine like terms: -17.755280905 + -0.5 = -18.255280905
x = -18.255280905

Simplifying
x = -18.255280905


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.255280905, -18.255280905}

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