k^2+22k+43=0

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Solution for k^2+22k+43=0 equation: 


Simplifying
k2 + 22k + 43 = 0

Reorder the terms:
43 + 22k + k2 = 0

Solving
43 + 22k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + 22k + -43 + k2 = 0 + -43

Reorder the terms:
43 + -43 + 22k + k2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 22k + k2 = 0 + -43
22k + k2 = 0 + -43

Combine like terms: 0 + -43 = -43
22k + k2 = -43

The k term is 22k.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22k + 121 + k2 = -43 + 121

Reorder the terms:
121 + 22k + k2 = -43 + 121

Combine like terms: -43 + 121 = 78
121 + 22k + k2 = 78

Factor a perfect square on the left side:
(k + 11)(k + 11) = 78

Calculate the square root of the right side: 8.831760866

Break this problem into two subproblems by setting 
(k + 11) equal to 8.831760866 and -8.831760866.


Subproblem 1
k + 11 = 8.831760866

Simplifying
k + 11 = 8.831760866

Reorder the terms:
11 + k = 8.831760866

Solving
11 + k = 8.831760866

Solving for variable 'k'.

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

Add '-11' to each side of the equation.
11 + -11 + k = 8.831760866 + -11

Combine like terms: 11 + -11 = 0
0 + k = 8.831760866 + -11
k = 8.831760866 + -11

Combine like terms: 8.831760866 + -11 = -2.168239134
k = -2.168239134

Simplifying
k = -2.168239134


Subproblem 2
k + 11 = -8.831760866

Simplifying
k + 11 = -8.831760866

Reorder the terms:
11 + k = -8.831760866

Solving
11 + k = -8.831760866

Solving for variable 'k'.

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

Add '-11' to each side of the equation.
11 + -11 + k = -8.831760866 + -11

Combine like terms: 11 + -11 = 0
0 + k = -8.831760866 + -11
k = -8.831760866 + -11

Combine like terms: -8.831760866 + -11 = -19.831760866
k = -19.831760866

Simplifying
k = -19.831760866


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-2.168239134, -19.831760866}

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