0=5k^2+2k+21

Solution for 0=5k^2+2k+21 equation:

Simplifying
0 = 5k2 + 2k + 21

Reorder the terms:
0 = 21 + 2k + 5k2

Solving
0 = 21 + 2k + 5k2

Solving for variable 'k'.

Combine like terms: 0 + -21 = -21
-21 + -2k + -5k2 = 21 + 2k + 5k2 + -21 + -2k + -5k2

Reorder the terms:
-21 + -2k + -5k2 = 21 + -21 + 2k + -2k + 5k2 + -5k2

Combine like terms: 21 + -21 = 0
-21 + -2k + -5k2 = 0 + 2k + -2k + 5k2 + -5k2
-21 + -2k + -5k2 = 2k + -2k + 5k2 + -5k2

Combine like terms: 2k + -2k = 0
-21 + -2k + -5k2 = 0 + 5k2 + -5k2
-21 + -2k + -5k2 = 5k2 + -5k2

Combine like terms: 5k2 + -5k2 = 0
-21 + -2k + -5k2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 2k + 5k2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(21 + 2k + 5k2)' equal to zero and attempt to solve:

Simplifying
21 + 2k + 5k2 = 0

Solving
21 + 2k + 5k2 = 0

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

Divide each side by '5'.
4.2 + 0.4k + k2 = 0

Move the constant term to the right:

Add '-4.2' to each side of the equation.
4.2 + 0.4k + -4.2 + k2 = 0 + -4.2

Reorder the terms:
4.2 + -4.2 + 0.4k + k2 = 0 + -4.2

Combine like terms: 4.2 + -4.2 = 0.0
0.0 + 0.4k + k2 = 0 + -4.2
0.4k + k2 = 0 + -4.2

Combine like terms: 0 + -4.2 = -4.2
0.4k + k2 = -4.2

The k term is 0.4k.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4k + 0.04 + k2 = -4.2 + 0.04

Reorder the terms:
0.04 + 0.4k + k2 = -4.2 + 0.04

Combine like terms: -4.2 + 0.04 = -4.16
0.04 + 0.4k + k2 = -4.16

Factor a perfect square on the left side:
(k + 0.2)(k + 0.2) = -4.16

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.