3x^2=-x-3

Solution for 3x^2=-x-3 equation:

Simplifying
3x2 = -1x + -3

Reorder the terms:
3x2 = -3 + -1x

Solving
3x2 = -3 + -1x

Solving for variable 'x'.

Reorder the terms:
3 + x + 3x2 = -3 + -1x + 3 + x

Reorder the terms:
3 + x + 3x2 = -3 + 3 + -1x + x

Combine like terms: -3 + 3 = 0
3 + x + 3x2 = 0 + -1x + x
3 + x + 3x2 = -1x + x

Combine like terms: -1x + x = 0
3 + x + 3x2 = 0

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

Divide each side by '3'.
1 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.3333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 0.3333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.3333333333x + x2 = 0 + -1
0.3333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.3333333333x + x2 = -1

The x term is x.  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.
0.3333333333x + 0.25 + x2 = -1 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + 0.3333333333x + x2 = -0.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.