r^2+2r+5=0

Solution for r^2+2r+5=0 equation:

Simplifying
r2 + 2r + 5 = 0

Reorder the terms:
5 + 2r + r2 = 0

Solving
5 + 2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 2r + -5 + r2 = 0 + -5

Reorder the terms:
5 + -5 + 2r + r2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2r + r2 = 0 + -5
2r + r2 = 0 + -5

Combine like terms: 0 + -5 = -5
2r + r2 = -5

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

Add '1' to each side of the equation.
2r + 1 + r2 = -5 + 1

Reorder the terms:
1 + 2r + r2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + 2r + r2 = -4

Factor a perfect square on the left side:
(r + 1)(r + 1) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.