x^2+18x+73=0

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Solution for x^2+18x+73=0 equation:


Simplifying
x2 + 18x + 73 = 0

Reorder the terms:
73 + 18x + x2 = 0

Solving
73 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-73' to each side of the equation.
73 + 18x + -73 + x2 = 0 + -73

Reorder the terms:
73 + -73 + 18x + x2 = 0 + -73

Combine like terms: 73 + -73 = 0
0 + 18x + x2 = 0 + -73
18x + x2 = 0 + -73

Combine like terms: 0 + -73 = -73
18x + x2 = -73

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 = -73 + 81

Reorder the terms:
81 + 18x + x2 = -73 + 81

Combine like terms: -73 + 81 = 8
81 + 18x + x2 = 8

Factor a perfect square on the left side:
(x + 9)(x + 9) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 9) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + 9 = 2.828427125

Simplifying
x + 9 = 2.828427125

Reorder the terms:
9 + x = 2.828427125

Solving
9 + x = 2.828427125

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 = 2.828427125 + -9

Combine like terms: 9 + -9 = 0
0 + x = 2.828427125 + -9
x = 2.828427125 + -9

Combine like terms: 2.828427125 + -9 = -6.171572875
x = -6.171572875

Simplifying
x = -6.171572875


Subproblem 2
x + 9 = -2.828427125

Simplifying
x + 9 = -2.828427125

Reorder the terms:
9 + x = -2.828427125

Solving
9 + x = -2.828427125

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 = -2.828427125 + -9

Combine like terms: 9 + -9 = 0
0 + x = -2.828427125 + -9
x = -2.828427125 + -9

Combine like terms: -2.828427125 + -9 = -11.828427125
x = -11.828427125

Simplifying
x = -11.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.171572875, -11.828427125}

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