x^2+18x+81=307

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Solution for x^2+18x+81=307 equation: 


Simplifying
x2 + 18x + 81 = 307

Reorder the terms:
81 + 18x + x2 = 307

Solving
81 + 18x + x2 = 307

Solving for variable 'x'.

Reorder the terms:
81 + -307 + 18x + x2 = 307 + -307

Combine like terms: 81 + -307 = -226
-226 + 18x + x2 = 307 + -307

Combine like terms: 307 + -307 = 0
-226 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '226' to each side of the equation.
-226 + 18x + 226 + x2 = 0 + 226

Reorder the terms:
-226 + 226 + 18x + x2 = 0 + 226

Combine like terms: -226 + 226 = 0
0 + 18x + x2 = 0 + 226
18x + x2 = 0 + 226

Combine like terms: 0 + 226 = 226
18x + x2 = 226

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 = 226 + 81

Reorder the terms:
81 + 18x + x2 = 226 + 81

Combine like terms: 226 + 81 = 307
81 + 18x + x2 = 307

Factor a perfect square on the left side:
(x + 9)(x + 9) = 307

Calculate the square root of the right side: 17.521415468

Break this problem into two subproblems by setting 
(x + 9) equal to 17.521415468 and -17.521415468.


Subproblem 1
x + 9 = 17.521415468

Simplifying
x + 9 = 17.521415468

Reorder the terms:
9 + x = 17.521415468

Solving
9 + x = 17.521415468

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 = 17.521415468 + -9

Combine like terms: 9 + -9 = 0
0 + x = 17.521415468 + -9
x = 17.521415468 + -9

Combine like terms: 17.521415468 + -9 = 8.521415468
x = 8.521415468

Simplifying
x = 8.521415468


Subproblem 2
x + 9 = -17.521415468

Simplifying
x + 9 = -17.521415468

Reorder the terms:
9 + x = -17.521415468

Solving
9 + x = -17.521415468

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 = -17.521415468 + -9

Combine like terms: 9 + -9 = 0
0 + x = -17.521415468 + -9
x = -17.521415468 + -9

Combine like terms: -17.521415468 + -9 = -26.521415468
x = -26.521415468

Simplifying
x = -26.521415468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.521415468, -26.521415468}

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