r^2+r+6=0

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

Simplifying
r2 + r + 6 = 0

Reorder the terms:
6 + r + r2 = 0

Solving
6 + r + 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 + r + -6 + r2 = 0 + -6

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

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

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

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
r + 0.25 + r2 = -6 + 0.25

Reorder the terms:
0.25 + r + r2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + r + r2 = -5.75

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.