Question

What are the solutions of 2x2 + 3x = -5

Answer 1

I don't see any way this one will factor. You will have to complete the square or use the quadratic formula.

Answer 2

If you are going to use the quadratic formula, make sure to put the problem into standard form. It looks to me that there are no real solutions, and that the roots are complex numbers.

Answer 3

Solution by completing the square.\[2x^2 + 3x = -5\]\[x^2+\frac{3x}{2}=\frac{-5}{2}\]\[x^2+\frac{3x}{2}+\frac{9}{16}=\frac{9}{16}-\frac{5}{2}\]\[(x+\frac{3}{4})^2=\frac{-31}{16}\]\[x+\frac{3}{4}= \pm \frac{\sqrt{31}i}{4}\]\[x=\frac{-3}{4} \pm \frac{\sqrt{31}i}{4}\]