(8+x)(5+x)=166.75

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Solution for (8+x)(5+x)=166.75 equation: 


Simplifying
(8 + x)(5 + x) = 166.75

Multiply (8 + x) * (5 + x)
(8(5 + x) + x(5 + x)) = 166.75
((5 * 8 + x * 8) + x(5 + x)) = 166.75
((40 + 8x) + x(5 + x)) = 166.75
(40 + 8x + (5 * x + x * x)) = 166.75
(40 + 8x + (5x + x2)) = 166.75

Combine like terms: 8x + 5x = 13x
(40 + 13x + x2) = 166.75

Solving
40 + 13x + x2 = 166.75

Solving for variable 'x'.

Reorder the terms:
40 + -166.75 + 13x + x2 = 166.75 + -166.75

Combine like terms: 40 + -166.75 = -126.75
-126.75 + 13x + x2 = 166.75 + -166.75

Combine like terms: 166.75 + -166.75 = 0.00
-126.75 + 13x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '126.75' to each side of the equation.
-126.75 + 13x + 126.75 + x2 = 0.00 + 126.75

Reorder the terms:
-126.75 + 126.75 + 13x + x2 = 0.00 + 126.75

Combine like terms: -126.75 + 126.75 = 0.00
0.00 + 13x + x2 = 0.00 + 126.75
13x + x2 = 0.00 + 126.75

Combine like terms: 0.00 + 126.75 = 126.75
13x + x2 = 126.75

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 126.75 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 126.75 + 42.25

Combine like terms: 126.75 + 42.25 = 169
42.25 + 13x + x2 = 169

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 169

Calculate the square root of the right side: 13

Break this problem into two subproblems by setting 
(x + 6.5) equal to 13 and -13.


Subproblem 1
x + 6.5 = 13

Simplifying
x + 6.5 = 13

Reorder the terms:
6.5 + x = 13

Solving
6.5 + x = 13

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 13 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 13 + -6.5
x = 13 + -6.5

Combine like terms: 13 + -6.5 = 6.5
x = 6.5

Simplifying
x = 6.5


Subproblem 2
x + 6.5 = -13

Simplifying
x + 6.5 = -13

Reorder the terms:
6.5 + x = -13

Solving
6.5 + x = -13

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -13 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -13 + -6.5
x = -13 + -6.5

Combine like terms: -13 + -6.5 = -19.5
x = -19.5

Simplifying
x = -19.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.5, -19.5}

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