x^2+18x+71=0

Solution for x^2+18x+71=0 equation:

Simplifying
x2 + 18x + 71 = 0

Reorder the terms:
71 + 18x + x2 = 0

Solving
71 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-71' to each side of the equation.
71 + 18x + -71 + x2 = 0 + -71

Reorder the terms:
71 + -71 + 18x + x2 = 0 + -71

Combine like terms: 71 + -71 = 0
0 + 18x + x2 = 0 + -71
18x + x2 = 0 + -71

Combine like terms: 0 + -71 = -71
18x + x2 = -71

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 = -71 + 81

Reorder the terms:
81 + 18x + x2 = -71 + 81

Combine like terms: -71 + 81 = 10
81 + 18x + x2 = 10

Factor a perfect square on the left side:
(x + 9)(x + 9) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 9) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + 9 = 3.16227766

Simplifying
x + 9 = 3.16227766

Reorder the terms:
9 + x = 3.16227766

Solving
9 + x = 3.16227766

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 = 3.16227766 + -9

Combine like terms: 9 + -9 = 0
0 + x = 3.16227766 + -9
x = 3.16227766 + -9

Combine like terms: 3.16227766 + -9 = -5.83772234
x = -5.83772234

Simplifying
x = -5.83772234

Subproblem 2
x + 9 = -3.16227766

Simplifying
x + 9 = -3.16227766

Reorder the terms:
9 + x = -3.16227766

Solving
9 + x = -3.16227766

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 = -3.16227766 + -9

Combine like terms: 9 + -9 = 0
0 + x = -3.16227766 + -9
x = -3.16227766 + -9

Combine like terms: -3.16227766 + -9 = -12.16227766
x = -12.16227766

Simplifying
x = -12.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.83772234, -12.16227766}