k^2-7k=-1

Solution for k^2-7k=-1 equation:

Simplifying
k2 + -7k = -1

Reorder the terms:
-7k + k2 = -1

Solving
-7k + k2 = -1

Solving for variable 'k'.

Reorder the terms:
1 + -7k + k2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -7k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -7k + -1 + k2 = 0 + -1

Reorder the terms:
1 + -1 + -7k + k2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7k + k2 = 0 + -1
-7k + k2 = 0 + -1

Combine like terms: 0 + -1 = -1
-7k + k2 = -1

The k term is -7k.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7k + 12.25 + k2 = -1 + 12.25

Reorder the terms:
12.25 + -7k + k2 = -1 + 12.25

Combine like terms: -1 + 12.25 = 11.25
12.25 + -7k + k2 = 11.25

Factor a perfect square on the left side:
(k + -3.5)(k + -3.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(k + -3.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
k + -3.5 = 3.354101966

Simplifying
k + -3.5 = 3.354101966

Reorder the terms:
-3.5 + k = 3.354101966

Solving
-3.5 + k = 3.354101966

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k = 3.354101966 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = 3.354101966 + 3.5
k = 3.354101966 + 3.5

Combine like terms: 3.354101966 + 3.5 = 6.854101966
k = 6.854101966

Simplifying
k = 6.854101966

Subproblem 2
k + -3.5 = -3.354101966

Simplifying
k + -3.5 = -3.354101966

Reorder the terms:
-3.5 + k = -3.354101966

Solving
-3.5 + k = -3.354101966

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k = -3.354101966 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = -3.354101966 + 3.5
k = -3.354101966 + 3.5

Combine like terms: -3.354101966 + 3.5 = 0.145898034
k = 0.145898034

Simplifying
k = 0.145898034

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {6.854101966, 0.145898034}