8k^2-16k+7=4

Solution for 8k^2-16k+7=4 equation:

Simplifying
8k2 + -16k + 7 = 4

Reorder the terms:
7 + -16k + 8k2 = 4

Solving
7 + -16k + 8k2 = 4

Solving for variable 'k'.

Reorder the terms:
7 + -4 + -16k + 8k2 = 4 + -4

Combine like terms: 7 + -4 = 3
3 + -16k + 8k2 = 4 + -4

Combine like terms: 4 + -4 = 0
3 + -16k + 8k2 = 0

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

Divide each side by '8'.
0.375 + -2k + k2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -2k + -0.375 + k2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -2k + k2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -2k + k2 = 0 + -0.375
-2k + k2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-2k + k2 = -0.375

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 = -0.375 + 1

Reorder the terms:
1 + -2k + k2 = -0.375 + 1

Combine like terms: -0.375 + 1 = 0.625
1 + -2k + k2 = 0.625

Factor a perfect square on the left side:
(k + -1)(k + -1) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(k + -1) equal to 0.790569415 and -0.790569415.

Subproblem 1
k + -1 = 0.790569415

Simplifying
k + -1 = 0.790569415

Reorder the terms:
-1 + k = 0.790569415

Solving
-1 + k = 0.790569415

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 = 0.790569415 + 1

Combine like terms: -1 + 1 = 0
0 + k = 0.790569415 + 1
k = 0.790569415 + 1

Combine like terms: 0.790569415 + 1 = 1.790569415
k = 1.790569415

Simplifying
k = 1.790569415

Subproblem 2
k + -1 = -0.790569415

Simplifying
k + -1 = -0.790569415

Reorder the terms:
-1 + k = -0.790569415

Solving
-1 + k = -0.790569415

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 = -0.790569415 + 1

Combine like terms: -1 + 1 = 0
0 + k = -0.790569415 + 1
k = -0.790569415 + 1

Combine like terms: -0.790569415 + 1 = 0.209430585
k = 0.209430585

Simplifying
k = 0.209430585

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.790569415, 0.209430585}