a^2+3a+6=0

Solution for a^2+3a+6=0 equation:

Simplifying
a2 + 3a + 6 = 0

Reorder the terms:
6 + 3a + a2 = 0

Solving
6 + 3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 3a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + 3a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 3a + a2 = 0 + -6
3a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
3a + a2 = -6

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = -6 + 2.25

Reorder the terms:
2.25 + 3a + a2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + 3a + a2 = -3.75

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.