5(k-2)8k=-34

Solution for 5(k-2)8k=-34 equation:

Simplifying
5(k + -2) * 8k = -34

Reorder the terms:
5(-2 + k) * 8k = -34

Reorder the terms for easier multiplication:
5 * 8k(-2 + k) = -34

Multiply 5 * 8
40k(-2 + k) = -34
(-2 * 40k + k * 40k) = -34
(-80k + 40k2) = -34

Solving
-80k + 40k2 = -34

Solving for variable 'k'.

Reorder the terms:
34 + -80k + 40k2 = -34 + 34

Combine like terms: -34 + 34 = 0
34 + -80k + 40k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -40k + 20k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(17 + -40k + 20k2)' equal to zero and attempt to solve:

Simplifying
17 + -40k + 20k2 = 0

Solving
17 + -40k + 20k2 = 0

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

Divide each side by '20'.
0.85 + -2k + k2 = 0.0

Move the constant term to the right:

Add '-0.85' to each side of the equation.
0.85 + -2k + -0.85 + k2 = 0.0 + -0.85

Reorder the terms:
0.85 + -0.85 + -2k + k2 = 0.0 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + -2k + k2 = 0.0 + -0.85
-2k + k2 = 0.0 + -0.85

Combine like terms: 0.0 + -0.85 = -0.85
-2k + k2 = -0.85

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = -0.85 + 1

Reorder the terms:
1 + -2k + k2 = -0.85 + 1

Combine like terms: -0.85 + 1 = 0.15
1 + -2k + k2 = 0.15

Factor a perfect square on the left side:
(k + -1)(k + -1) = 0.15

Calculate the square root of the right side: 0.387298335

Break this problem into two subproblems by setting 
(k + -1) equal to 0.387298335 and -0.387298335.

Subproblem 1
k + -1 = 0.387298335

Simplifying
k + -1 = 0.387298335

Reorder the terms:
-1 + k = 0.387298335

Solving
-1 + k = 0.387298335

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 0.387298335 + 1

Combine like terms: -1 + 1 = 0
0 + k = 0.387298335 + 1
k = 0.387298335 + 1

Combine like terms: 0.387298335 + 1 = 1.387298335
k = 1.387298335

Simplifying
k = 1.387298335

Subproblem 2
k + -1 = -0.387298335

Simplifying
k + -1 = -0.387298335

Reorder the terms:
-1 + k = -0.387298335

Solving
-1 + k = -0.387298335

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -0.387298335 + 1

Combine like terms: -1 + 1 = 0
0 + k = -0.387298335 + 1
k = -0.387298335 + 1

Combine like terms: -0.387298335 + 1 = 0.612701665
k = 0.612701665

Simplifying
k = 0.612701665

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.387298335, 0.612701665}
Solution
k = {1.387298335, 0.612701665}