x^2+18x+81=30

Solution for x^2+18x+81=30 equation:

Simplifying
x2 + 18x + 81 = 30

Reorder the terms:
81 + 18x + x2 = 30

Solving
81 + 18x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
81 + -30 + 18x + x2 = 30 + -30

Combine like terms: 81 + -30 = 51
51 + 18x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
51 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-51' to each side of the equation.
51 + 18x + -51 + x2 = 0 + -51

Reorder the terms:
51 + -51 + 18x + x2 = 0 + -51

Combine like terms: 51 + -51 = 0
0 + 18x + x2 = 0 + -51
18x + x2 = 0 + -51

Combine like terms: 0 + -51 = -51
18x + x2 = -51

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -51 + 81

Reorder the terms:
81 + 18x + x2 = -51 + 81

Combine like terms: -51 + 81 = 30
81 + 18x + x2 = 30

Factor a perfect square on the left side:
(x + 9)(x + 9) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + 9) equal to 5.477225575 and -5.477225575.

Subproblem 1
x + 9 = 5.477225575

Simplifying
x + 9 = 5.477225575

Reorder the terms:
9 + x = 5.477225575

Solving
9 + x = 5.477225575

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + x = 5.477225575 + -9

Combine like terms: 9 + -9 = 0
0 + x = 5.477225575 + -9
x = 5.477225575 + -9

Combine like terms: 5.477225575 + -9 = -3.522774425
x = -3.522774425

Simplifying
x = -3.522774425

Subproblem 2
x + 9 = -5.477225575

Simplifying
x + 9 = -5.477225575

Reorder the terms:
9 + x = -5.477225575

Solving
9 + x = -5.477225575

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + x = -5.477225575 + -9

Combine like terms: 9 + -9 = 0
0 + x = -5.477225575 + -9
x = -5.477225575 + -9

Combine like terms: -5.477225575 + -9 = -14.477225575
x = -14.477225575

Simplifying
x = -14.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.522774425, -14.477225575}