x^2+30x+2=0

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


Simplifying
x2 + 30x + 2 = 0

Reorder the terms:
2 + 30x + x2 = 0

Solving
2 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 30x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 30x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 30x + x2 = 0 + -2
30x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
30x + x2 = -2

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 = -2 + 225

Reorder the terms:
225 + 30x + x2 = -2 + 225

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

Factor a perfect square on the left side:
(x + 15)(x + 15) = 223

Calculate the square root of the right side: 14.933184523

Break this problem into two subproblems by setting 
(x + 15) equal to 14.933184523 and -14.933184523.


Subproblem 1
x + 15 = 14.933184523

Simplifying
x + 15 = 14.933184523

Reorder the terms:
15 + x = 14.933184523

Solving
15 + x = 14.933184523

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 = 14.933184523 + -15

Combine like terms: 15 + -15 = 0
0 + x = 14.933184523 + -15
x = 14.933184523 + -15

Combine like terms: 14.933184523 + -15 = -0.066815477
x = -0.066815477

Simplifying
x = -0.066815477


Subproblem 2
x + 15 = -14.933184523

Simplifying
x + 15 = -14.933184523

Reorder the terms:
15 + x = -14.933184523

Solving
15 + x = -14.933184523

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 = -14.933184523 + -15

Combine like terms: 15 + -15 = 0
0 + x = -14.933184523 + -15
x = -14.933184523 + -15

Combine like terms: -14.933184523 + -15 = -29.933184523
x = -29.933184523

Simplifying
x = -29.933184523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.066815477, -29.933184523}

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