x^2+30x+207=0

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Solution for x^2+30x+207=0 equation: 


Simplifying
x2 + 30x + 207 = 0

Reorder the terms:
207 + 30x + x2 = 0

Solving
207 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-207' to each side of the equation.
207 + 30x + -207 + x2 = 0 + -207

Reorder the terms:
207 + -207 + 30x + x2 = 0 + -207

Combine like terms: 207 + -207 = 0
0 + 30x + x2 = 0 + -207
30x + x2 = 0 + -207

Combine like terms: 0 + -207 = -207
30x + x2 = -207

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 = -207 + 225

Reorder the terms:
225 + 30x + x2 = -207 + 225

Combine like terms: -207 + 225 = 18
225 + 30x + x2 = 18

Factor a perfect square on the left side:
(x + 15)(x + 15) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 15) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 15 = 4.242640687

Simplifying
x + 15 = 4.242640687

Reorder the terms:
15 + x = 4.242640687

Solving
15 + x = 4.242640687

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 = 4.242640687 + -15

Combine like terms: 15 + -15 = 0
0 + x = 4.242640687 + -15
x = 4.242640687 + -15

Combine like terms: 4.242640687 + -15 = -10.757359313
x = -10.757359313

Simplifying
x = -10.757359313


Subproblem 2
x + 15 = -4.242640687

Simplifying
x + 15 = -4.242640687

Reorder the terms:
15 + x = -4.242640687

Solving
15 + x = -4.242640687

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 = -4.242640687 + -15

Combine like terms: 15 + -15 = 0
0 + x = -4.242640687 + -15
x = -4.242640687 + -15

Combine like terms: -4.242640687 + -15 = -19.242640687
x = -19.242640687

Simplifying
x = -19.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-10.757359313, -19.242640687}

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