-k^2+2k-1+7=-43

Solution for -k^2+2k-1+7=-43 equation:

Simplifying
-1k2 + 2k + -1 + 7 = -43

Reorder the terms:
-1 + 7 + 2k + -1k2 = -43

Combine like terms: -1 + 7 = 6
6 + 2k + -1k2 = -43

Solving
6 + 2k + -1k2 = -43

Solving for variable 'k'.

Reorder the terms:
6 + 43 + 2k + -1k2 = -43 + 43

Combine like terms: 6 + 43 = 49
49 + 2k + -1k2 = -43 + 43

Combine like terms: -43 + 43 = 0
49 + 2k + -1k2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-49 + -2k + k2 = 0

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -2k + 49 + k2 = 0 + 49

Reorder the terms:
-49 + 49 + -2k + k2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -2k + k2 = 0 + 49
-2k + k2 = 0 + 49

Combine like terms: 0 + 49 = 49
-2k + k2 = 49

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 = 49 + 1

Reorder the terms:
1 + -2k + k2 = 49 + 1

Combine like terms: 49 + 1 = 50
1 + -2k + k2 = 50

Factor a perfect square on the left side:
(k + -1)(k + -1) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(k + -1) equal to 7.071067812 and -7.071067812.

Subproblem 1
k + -1 = 7.071067812

Simplifying
k + -1 = 7.071067812

Reorder the terms:
-1 + k = 7.071067812

Solving
-1 + k = 7.071067812

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 = 7.071067812 + 1

Combine like terms: -1 + 1 = 0
0 + k = 7.071067812 + 1
k = 7.071067812 + 1

Combine like terms: 7.071067812 + 1 = 8.071067812
k = 8.071067812

Simplifying
k = 8.071067812

Subproblem 2
k + -1 = -7.071067812

Simplifying
k + -1 = -7.071067812

Reorder the terms:
-1 + k = -7.071067812

Solving
-1 + k = -7.071067812

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 = -7.071067812 + 1

Combine like terms: -1 + 1 = 0
0 + k = -7.071067812 + 1
k = -7.071067812 + 1

Combine like terms: -7.071067812 + 1 = -6.071067812
k = -6.071067812

Simplifying
k = -6.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {8.071067812, -6.071067812}