x^2+30x+11=0

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Solution for x^2+30x+11=0 equation: 


Simplifying
x2 + 30x + 11 = 0

Reorder the terms:
11 + 30x + x2 = 0

Solving
11 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 30x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 30x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 30x + x2 = 0 + -11
30x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
30x + x2 = -11

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 = -11 + 225

Reorder the terms:
225 + 30x + x2 = -11 + 225

Combine like terms: -11 + 225 = 214
225 + 30x + x2 = 214

Factor a perfect square on the left side:
(x + 15)(x + 15) = 214

Calculate the square root of the right side: 14.628738838

Break this problem into two subproblems by setting 
(x + 15) equal to 14.628738838 and -14.628738838.


Subproblem 1
x + 15 = 14.628738838

Simplifying
x + 15 = 14.628738838

Reorder the terms:
15 + x = 14.628738838

Solving
15 + x = 14.628738838

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 = 14.628738838 + -15

Combine like terms: 15 + -15 = 0
0 + x = 14.628738838 + -15
x = 14.628738838 + -15

Combine like terms: 14.628738838 + -15 = -0.371261162
x = -0.371261162

Simplifying
x = -0.371261162


Subproblem 2
x + 15 = -14.628738838

Simplifying
x + 15 = -14.628738838

Reorder the terms:
15 + x = -14.628738838

Solving
15 + x = -14.628738838

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 = -14.628738838 + -15

Combine like terms: 15 + -15 = 0
0 + x = -14.628738838 + -15
x = -14.628738838 + -15

Combine like terms: -14.628738838 + -15 = -29.628738838
x = -29.628738838

Simplifying
x = -29.628738838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.371261162, -29.628738838}

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