x^2+30x+222=0

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Solution for x^2+30x+222=0 equation: 


Simplifying
x2 + 30x + 222 = 0

Reorder the terms:
222 + 30x + x2 = 0

Solving
222 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-222' to each side of the equation.
222 + 30x + -222 + x2 = 0 + -222

Reorder the terms:
222 + -222 + 30x + x2 = 0 + -222

Combine like terms: 222 + -222 = 0
0 + 30x + x2 = 0 + -222
30x + x2 = 0 + -222

Combine like terms: 0 + -222 = -222
30x + x2 = -222

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -222 + 225

Reorder the terms:
225 + 30x + x2 = -222 + 225

Combine like terms: -222 + 225 = 3
225 + 30x + x2 = 3

Factor a perfect square on the left side:
(x + 15)(x + 15) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 15) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + 15 = 1.732050808

Simplifying
x + 15 = 1.732050808

Reorder the terms:
15 + x = 1.732050808

Solving
15 + x = 1.732050808

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 1.732050808 + -15

Combine like terms: 15 + -15 = 0
0 + x = 1.732050808 + -15
x = 1.732050808 + -15

Combine like terms: 1.732050808 + -15 = -13.267949192
x = -13.267949192

Simplifying
x = -13.267949192


Subproblem 2
x + 15 = -1.732050808

Simplifying
x + 15 = -1.732050808

Reorder the terms:
15 + x = -1.732050808

Solving
15 + x = -1.732050808

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -1.732050808 + -15

Combine like terms: 15 + -15 = 0
0 + x = -1.732050808 + -15
x = -1.732050808 + -15

Combine like terms: -1.732050808 + -15 = -16.732050808
x = -16.732050808

Simplifying
x = -16.732050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-13.267949192, -16.732050808}

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