x^2+30x+210=0

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Solution for x^2+30x+210=0 equation: 


Simplifying
x2 + 30x + 210 = 0

Reorder the terms:
210 + 30x + x2 = 0

Solving
210 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-210' to each side of the equation.
210 + 30x + -210 + x2 = 0 + -210

Reorder the terms:
210 + -210 + 30x + x2 = 0 + -210

Combine like terms: 210 + -210 = 0
0 + 30x + x2 = 0 + -210
30x + x2 = 0 + -210

Combine like terms: 0 + -210 = -210
30x + x2 = -210

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 = -210 + 225

Reorder the terms:
225 + 30x + x2 = -210 + 225

Combine like terms: -210 + 225 = 15
225 + 30x + x2 = 15

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

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 15) equal to 3.872983346 and -3.872983346.


Subproblem 1
x + 15 = 3.872983346

Simplifying
x + 15 = 3.872983346

Reorder the terms:
15 + x = 3.872983346

Solving
15 + x = 3.872983346

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 = 3.872983346 + -15

Combine like terms: 15 + -15 = 0
0 + x = 3.872983346 + -15
x = 3.872983346 + -15

Combine like terms: 3.872983346 + -15 = -11.127016654
x = -11.127016654

Simplifying
x = -11.127016654


Subproblem 2
x + 15 = -3.872983346

Simplifying
x + 15 = -3.872983346

Reorder the terms:
15 + x = -3.872983346

Solving
15 + x = -3.872983346

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 = -3.872983346 + -15

Combine like terms: 15 + -15 = 0
0 + x = -3.872983346 + -15
x = -3.872983346 + -15

Combine like terms: -3.872983346 + -15 = -18.872983346
x = -18.872983346

Simplifying
x = -18.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-11.127016654, -18.872983346}

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