-8k^2-2k+7=0

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Solution for -8k^2-2k+7=0 equation: 


Simplifying
-8k2 + -2k + 7 = 0

Reorder the terms:
7 + -2k + -8k2 = 0

Solving
7 + -2k + -8k2 = 0

Solving for variable 'k'.

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

Divide each side by '-8'.
-0.875 + 0.25k + k2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + 0.25k + 0.875 + k2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + 0.25k + k2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + 0.25k + k2 = 0 + 0.875
0.25k + k2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
0.25k + k2 = 0.875

The k term is 0.25k.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25k + 0.015625 + k2 = 0.875 + 0.015625

Reorder the terms:
0.015625 + 0.25k + k2 = 0.875 + 0.015625

Combine like terms: 0.875 + 0.015625 = 0.890625
0.015625 + 0.25k + k2 = 0.890625

Factor a perfect square on the left side:
(k + 0.125)(k + 0.125) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(k + 0.125) equal to 0.943729304 and -0.943729304.


Subproblem 1
k + 0.125 = 0.943729304

Simplifying
k + 0.125 = 0.943729304

Reorder the terms:
0.125 + k = 0.943729304

Solving
0.125 + k = 0.943729304

Solving for variable 'k'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + k = 0.943729304 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + k = 0.943729304 + -0.125
k = 0.943729304 + -0.125

Combine like terms: 0.943729304 + -0.125 = 0.818729304
k = 0.818729304

Simplifying
k = 0.818729304


Subproblem 2
k + 0.125 = -0.943729304

Simplifying
k + 0.125 = -0.943729304

Reorder the terms:
0.125 + k = -0.943729304

Solving
0.125 + k = -0.943729304

Solving for variable 'k'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + k = -0.943729304 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + k = -0.943729304 + -0.125
k = -0.943729304 + -0.125

Combine like terms: -0.943729304 + -0.125 = -1.068729304
k = -1.068729304

Simplifying
k = -1.068729304


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.818729304, -1.068729304}

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