k^2+6k-21=0

Solution for k^2+6k-21=0 equation:

Simplifying
k2 + 6k + -21 = 0

Reorder the terms:
-21 + 6k + k2 = 0

Solving
-21 + 6k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 6k + 21 + k2 = 0 + 21

Reorder the terms:
-21 + 21 + 6k + k2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 6k + k2 = 0 + 21
6k + k2 = 0 + 21

Combine like terms: 0 + 21 = 21
6k + k2 = 21

The k term is 6k.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6k + 9 + k2 = 21 + 9

Reorder the terms:
9 + 6k + k2 = 21 + 9

Combine like terms: 21 + 9 = 30
9 + 6k + k2 = 30

Factor a perfect square on the left side:
(k + 3)(k + 3) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(k + 3) equal to 5.477225575 and -5.477225575.

Subproblem 1
k + 3 = 5.477225575

Simplifying
k + 3 = 5.477225575

Reorder the terms:
3 + k = 5.477225575

Solving
3 + k = 5.477225575

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = 5.477225575 + -3

Combine like terms: 3 + -3 = 0
0 + k = 5.477225575 + -3
k = 5.477225575 + -3

Combine like terms: 5.477225575 + -3 = 2.477225575
k = 2.477225575

Simplifying
k = 2.477225575

Subproblem 2
k + 3 = -5.477225575

Simplifying
k + 3 = -5.477225575

Reorder the terms:
3 + k = -5.477225575

Solving
3 + k = -5.477225575

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = -5.477225575 + -3

Combine like terms: 3 + -3 = 0
0 + k = -5.477225575 + -3
k = -5.477225575 + -3

Combine like terms: -5.477225575 + -3 = -8.477225575
k = -8.477225575

Simplifying
k = -8.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.477225575, -8.477225575}