18x-x^2=71

Solution for 18x-x^2=71 equation:

Simplifying
18x + -1x2 = 71

Solving
18x + -1x2 = 71

Solving for variable 'x'.

Reorder the terms:
-71 + 18x + -1x2 = 71 + -71

Combine like terms: 71 + -71 = 0
-71 + 18x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
71 + -18x + x2 = 0

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 = 12.16227766
x = 12.16227766

Simplifying
x = 12.16227766

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 = 5.83772234
x = 5.83772234

Simplifying
x = 5.83772234

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