p^2+2p+21=0

Solution for p^2+2p+21=0 equation:

Simplifying
p2 + 2p + 21 = 0

Reorder the terms:
21 + 2p + p2 = 0

Solving
21 + 2p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 2p + -21 + p2 = 0 + -21

Reorder the terms:
21 + -21 + 2p + p2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 2p + p2 = 0 + -21
2p + p2 = 0 + -21

Combine like terms: 0 + -21 = -21
2p + p2 = -21

The p term is 2p.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2p + 1 + p2 = -21 + 1

Reorder the terms:
1 + 2p + p2 = -21 + 1

Combine like terms: -21 + 1 = -20
1 + 2p + p2 = -20

Factor a perfect square on the left side:
(p + 1)(p + 1) = -20

Can't calculate square root of the right side.

The solution to this equation could not be determined.