Question

Solve y^2 + 3y = -1 -PlushDNA

Answer 1

Answer:

$y=-\frac{3+\sqrt{5}}{2}$ AND $y=-\frac{3-\sqrt{5}}{2}$

Step-by-step explanation:

Given: $y^2+3y=-1$

To solve for $y$, we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:

$y^2+3y+1=0$

We can solve for $y$ by using the quadratic formula:

$y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}$ AND $y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}$

Let's identify our values:

$a: 1\\b: 3\\c: 1$

Plug in the values and simplify.

$y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}$

Your final answers are:

$y=-\frac{3+\sqrt{5}}{2}$ AND $y=-\frac{3-\sqrt{5}}{2}$