x^2+30x+223=0

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Solution for x^2+30x+223=0 equation: 


Simplifying
x2 + 30x + 223 = 0

Reorder the terms:
223 + 30x + x2 = 0

Solving
223 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-223' to each side of the equation.
223 + 30x + -223 + x2 = 0 + -223

Reorder the terms:
223 + -223 + 30x + x2 = 0 + -223

Combine like terms: 223 + -223 = 0
0 + 30x + x2 = 0 + -223
30x + x2 = 0 + -223

Combine like terms: 0 + -223 = -223
30x + x2 = -223

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 = -223 + 225

Reorder the terms:
225 + 30x + x2 = -223 + 225

Combine like terms: -223 + 225 = 2
225 + 30x + x2 = 2

Factor a perfect square on the left side:
(x + 15)(x + 15) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 15) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + 15 = 1.414213562

Simplifying
x + 15 = 1.414213562

Reorder the terms:
15 + x = 1.414213562

Solving
15 + x = 1.414213562

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 = 1.414213562 + -15

Combine like terms: 15 + -15 = 0
0 + x = 1.414213562 + -15
x = 1.414213562 + -15

Combine like terms: 1.414213562 + -15 = -13.585786438
x = -13.585786438

Simplifying
x = -13.585786438


Subproblem 2
x + 15 = -1.414213562

Simplifying
x + 15 = -1.414213562

Reorder the terms:
15 + x = -1.414213562

Solving
15 + x = -1.414213562

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 = -1.414213562 + -15

Combine like terms: 15 + -15 = 0
0 + x = -1.414213562 + -15
x = -1.414213562 + -15

Combine like terms: -1.414213562 + -15 = -16.414213562
x = -16.414213562

Simplifying
x = -16.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-13.585786438, -16.414213562}

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