27=0.5*(x-9)(x-9)

Solution for 27=0.5*(x-9)(x-9) equation:

Simplifying
27 = 0.5(x + -9)(x + -9)

Reorder the terms:
27 = 0.5(-9 + x)(x + -9)

Reorder the terms:
27 = 0.5(-9 + x)(-9 + x)

Multiply (-9 + x) * (-9 + x)
27 = 0.5(-9(-9 + x) + x(-9 + x))
27 = 0.5((-9 * -9 + x * -9) + x(-9 + x))
27 = 0.5((81 + -9x) + x(-9 + x))
27 = 0.5(81 + -9x + (-9 * x + x * x))
27 = 0.5(81 + -9x + (-9x + x2))

Combine like terms: -9x + -9x = -18x
27 = 0.5(81 + -18x + x2)
27 = (81 * 0.5 + -18x * 0.5 + x2 * 0.5)
27 = (40.5 + -9x + 0.5x2)

Solving
27 = 40.5 + -9x + 0.5x2

Solving for variable 'x'.

Combine like terms: 27 + -40.5 = -13.5
-13.5 + 9x + -0.5x2 = 40.5 + -9x + 0.5x2 + -40.5 + 9x + -0.5x2

Reorder the terms:
-13.5 + 9x + -0.5x2 = 40.5 + -40.5 + -9x + 9x + 0.5x2 + -0.5x2

Combine like terms: 40.5 + -40.5 = 0.0
-13.5 + 9x + -0.5x2 = 0.0 + -9x + 9x + 0.5x2 + -0.5x2
-13.5 + 9x + -0.5x2 = -9x + 9x + 0.5x2 + -0.5x2

Combine like terms: -9x + 9x = 0
-13.5 + 9x + -0.5x2 = 0 + 0.5x2 + -0.5x2
-13.5 + 9x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
-13.5 + 9x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
27 + -18x + x2 = 0

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -18x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + -18x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -18x + x2 = 0 + -27
-18x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-18x + x2 = -27

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 = -27 + 81

Reorder the terms:
81 + -18x + x2 = -27 + 81

Combine like terms: -27 + 81 = 54
81 + -18x + x2 = 54

Factor a perfect square on the left side:
(x + -9)(x + -9) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + -9) equal to 7.348469228 and -7.348469228.

Subproblem 1
x + -9 = 7.348469228

Simplifying
x + -9 = 7.348469228

Reorder the terms:
-9 + x = 7.348469228

Solving
-9 + x = 7.348469228

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 = 7.348469228 + 9

Combine like terms: -9 + 9 = 0
0 + x = 7.348469228 + 9
x = 7.348469228 + 9

Combine like terms: 7.348469228 + 9 = 16.348469228
x = 16.348469228

Simplifying
x = 16.348469228

Subproblem 2
x + -9 = -7.348469228

Simplifying
x + -9 = -7.348469228

Reorder the terms:
-9 + x = -7.348469228

Solving
-9 + x = -7.348469228

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 = -7.348469228 + 9

Combine like terms: -9 + 9 = 0
0 + x = -7.348469228 + 9
x = -7.348469228 + 9

Combine like terms: -7.348469228 + 9 = 1.651530772
x = 1.651530772

Simplifying
x = 1.651530772

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.348469228, 1.651530772}