r^2+4r+6=0

Solution for r^2+4r+6=0 equation:

Simplifying
r2 + 4r + 6 = 0

Reorder the terms:
6 + 4r + r2 = 0

Solving
6 + 4r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 4r + -6 + r2 = 0 + -6

Reorder the terms:
6 + -6 + 4r + r2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 4r + r2 = 0 + -6
4r + r2 = 0 + -6

Combine like terms: 0 + -6 = -6
4r + r2 = -6

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = -6 + 4

Reorder the terms:
4 + 4r + r2 = -6 + 4

Combine like terms: -6 + 4 = -2
4 + 4r + r2 = -2

Factor a perfect square on the left side:
(r + 2)(r + 2) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.