(x-8)(x-1.67)=0

Solution for (x-8)(x-1.67)=0 equation:

Simplifying
(x + -8)(x + -1.67) = 0

Reorder the terms:
(-8 + x)(x + -1.67) = 0

Reorder the terms:
(-8 + x)(-1.67 + x) = 0

Multiply (-8 + x) * (-1.67 + x)
(-8(-1.67 + x) + x(-1.67 + x)) = 0
((-1.67 * -8 + x * -8) + x(-1.67 + x)) = 0
((13.36 + -8x) + x(-1.67 + x)) = 0
(13.36 + -8x + (-1.67 * x + x * x)) = 0
(13.36 + -8x + (-1.67x + x2)) = 0

Combine like terms: -8x + -1.67x = -9.67x
(13.36 + -9.67x + x2) = 0

Solving
13.36 + -9.67x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-13.36' to each side of the equation.
13.36 + -9.67x + -13.36 + x2 = 0 + -13.36

Reorder the terms:
13.36 + -13.36 + -9.67x + x2 = 0 + -13.36

Combine like terms: 13.36 + -13.36 = 0.00
0.00 + -9.67x + x2 = 0 + -13.36
-9.67x + x2 = 0 + -13.36

Combine like terms: 0 + -13.36 = -13.36
-9.67x + x2 = -13.36

The x term is -9.67x.  Take half its coefficient (-4.835).
Square it (23.377225) and add it to both sides.

Add '23.377225' to each side of the equation.
-9.67x + 23.377225 + x2 = -13.36 + 23.377225

Reorder the terms:
23.377225 + -9.67x + x2 = -13.36 + 23.377225

Combine like terms: -13.36 + 23.377225 = 10.017225
23.377225 + -9.67x + x2 = 10.017225

Factor a perfect square on the left side:
(x + -4.835)(x + -4.835) = 10.017225

Calculate the square root of the right side: 3.165

Break this problem into two subproblems by setting 
(x + -4.835) equal to 3.165 and -3.165.

Subproblem 1
x + -4.835 = 3.165

Simplifying
x + -4.835 = 3.165

Reorder the terms:
-4.835 + x = 3.165

Solving
-4.835 + x = 3.165

Solving for variable 'x'.

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

Add '4.835' to each side of the equation.
-4.835 + 4.835 + x = 3.165 + 4.835

Combine like terms: -4.835 + 4.835 = 0.000
0.000 + x = 3.165 + 4.835
x = 3.165 + 4.835

Combine like terms: 3.165 + 4.835 = 8
x = 8

Simplifying
x = 8

Subproblem 2
x + -4.835 = -3.165

Simplifying
x + -4.835 = -3.165

Reorder the terms:
-4.835 + x = -3.165

Solving
-4.835 + x = -3.165

Solving for variable 'x'.

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

Add '4.835' to each side of the equation.
-4.835 + 4.835 + x = -3.165 + 4.835

Combine like terms: -4.835 + 4.835 = 0.000
0.000 + x = -3.165 + 4.835
x = -3.165 + 4.835

Combine like terms: -3.165 + 4.835 = 1.67
x = 1.67

Simplifying
x = 1.67

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8, 1.67}