3a^2+a+6=0

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


Simplifying
3a2 + a + 6 = 0

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

Solving
6 + a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
2 + 0.3333333333a + a2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.3333333333a + -2 + a2 = 0 + -2

Reorder the terms:
2 + -2 + 0.3333333333a + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.3333333333a + a2 = 0 + -2
0.3333333333a + a2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.3333333333a + a2 = -2

The a term is a.  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.
0.3333333333a + 0.25 + a2 = -2 + 0.25

Reorder the terms:
0.25 + 0.3333333333a + a2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + 0.3333333333a + a2 = -1.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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