52=.5((x+6)*(x+5))

Solution for 52=.5((x+6)*(x+5)) equation:

Simplifying
52 = 0.5((x + 6)(x + 5))

Reorder the terms:
52 = 0.5((6 + x)(x + 5))

Reorder the terms:
52 = 0.5((6 + x)(5 + x))

Multiply (6 + x) * (5 + x)
52 = 0.5((6(5 + x) + x(5 + x)))
52 = 0.5(((5 * 6 + x * 6) + x(5 + x)))
52 = 0.5(((30 + 6x) + x(5 + x)))
52 = 0.5((30 + 6x + (5 * x + x * x)))
52 = 0.5((30 + 6x + (5x + x2)))

Combine like terms: 6x + 5x = 11x
52 = 0.5((30 + 11x + x2))
52 = (30 * 0.5 + 11x * 0.5 + x2 * 0.5)
52 = (15 + 5.5x + 0.5x2)

Solving
52 = 15 + 5.5x + 0.5x2

Solving for variable 'x'.

Combine like terms: 52 + -15 = 37
37 + -5.5x + -0.5x2 = 15 + 5.5x + 0.5x2 + -15 + -5.5x + -0.5x2

Reorder the terms:
37 + -5.5x + -0.5x2 = 15 + -15 + 5.5x + -5.5x + 0.5x2 + -0.5x2

Combine like terms: 15 + -15 = 0
37 + -5.5x + -0.5x2 = 0 + 5.5x + -5.5x + 0.5x2 + -0.5x2
37 + -5.5x + -0.5x2 = 5.5x + -5.5x + 0.5x2 + -0.5x2

Combine like terms: 5.5x + -5.5x = 0.0
37 + -5.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2
37 + -5.5x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
37 + -5.5x + -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'.
-74 + 11x + x2 = 0

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + 11x + 74 + x2 = 0 + 74

Reorder the terms:
-74 + 74 + 11x + x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + 11x + x2 = 0 + 74
11x + x2 = 0 + 74

Combine like terms: 0 + 74 = 74
11x + x2 = 74

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 74 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 74 + 30.25

Combine like terms: 74 + 30.25 = 104.25
30.25 + 11x + x2 = 104.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 104.25

Calculate the square root of the right side: 10.210288928

Break this problem into two subproblems by setting 
(x + 5.5) equal to 10.210288928 and -10.210288928.

Subproblem 1
x + 5.5 = 10.210288928

Simplifying
x + 5.5 = 10.210288928

Reorder the terms:
5.5 + x = 10.210288928

Solving
5.5 + x = 10.210288928

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 10.210288928 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 10.210288928 + -5.5
x = 10.210288928 + -5.5

Combine like terms: 10.210288928 + -5.5 = 4.710288928
x = 4.710288928

Simplifying
x = 4.710288928

Subproblem 2
x + 5.5 = -10.210288928

Simplifying
x + 5.5 = -10.210288928

Reorder the terms:
5.5 + x = -10.210288928

Solving
5.5 + x = -10.210288928

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -10.210288928 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -10.210288928 + -5.5
x = -10.210288928 + -5.5

Combine like terms: -10.210288928 + -5.5 = -15.710288928
x = -15.710288928

Simplifying
x = -15.710288928

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.710288928, -15.710288928}