2m^2+1+4m^2+m+2=0

Solution for 2m^2+1+4m^2+m+2=0 equation:

Simplifying
2m2 + 1 + 4m2 + m + 2 = 0

Reorder the terms:
1 + 2 + m + 2m2 + 4m2 = 0

Combine like terms: 1 + 2 = 3
3 + m + 2m2 + 4m2 = 0

Combine like terms: 2m2 + 4m2 = 6m2
3 + m + 6m2 = 0

Solving
3 + m + 6m2 = 0

Solving for variable 'm'.

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

Divide each side by '6'.
0.5 + 0.1666666667m + m2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.1666666667m + -0.5 + m2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.1666666667m + m2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.1666666667m + m2 = 0 + -0.5
0.1666666667m + m2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.1666666667m + m2 = -0.5

The m term is m.  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.
0.1666666667m + 0.25 + m2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.1666666667m + m2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.1666666667m + m2 = -0.25

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.