x^2+x-228=0

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Solution for x^2+x-228=0 equation: 


Simplifying
x2 + x + -228 = 0

Reorder the terms:
-228 + x + x2 = 0

Solving
-228 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '228' to each side of the equation.
-228 + x + 228 + x2 = 0 + 228

Reorder the terms:
-228 + 228 + x + x2 = 0 + 228

Combine like terms: -228 + 228 = 0
0 + x + x2 = 0 + 228
x + x2 = 0 + 228

Combine like terms: 0 + 228 = 228
x + x2 = 228

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 = 228 + 0.25

Reorder the terms:
0.25 + x + x2 = 228 + 0.25

Combine like terms: 228 + 0.25 = 228.25
0.25 + x + x2 = 228.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 228.25

Calculate the square root of the right side: 15.10794493

Break this problem into two subproblems by setting 
(x + 0.5) equal to 15.10794493 and -15.10794493.


Subproblem 1
x + 0.5 = 15.10794493

Simplifying
x + 0.5 = 15.10794493

Reorder the terms:
0.5 + x = 15.10794493

Solving
0.5 + x = 15.10794493

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 = 15.10794493 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 15.10794493 + -0.5
x = 15.10794493 + -0.5

Combine like terms: 15.10794493 + -0.5 = 14.60794493
x = 14.60794493

Simplifying
x = 14.60794493


Subproblem 2
x + 0.5 = -15.10794493

Simplifying
x + 0.5 = -15.10794493

Reorder the terms:
0.5 + x = -15.10794493

Solving
0.5 + x = -15.10794493

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 = -15.10794493 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -15.10794493 + -0.5
x = -15.10794493 + -0.5

Combine like terms: -15.10794493 + -0.5 = -15.60794493
x = -15.60794493

Simplifying
x = -15.60794493


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.60794493, -15.60794493}

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