Question

Solve

y^2 + 3y = -1



-PlushDNA

Answer 1

`y=-(3+√(5))/(2)` AND
`y=-(3-√(5))/(2)`

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=(-b+√((b)^2-4(a)(c)))/(2a)` AND
`y=(-b-√((b)^2-4(a)(c)))/(2a)`

Let's identify our values:

`a: 1\\b: 3\\c: 1`

Plug in the values and simplify.

`y=(-3+√((3)^2-4(1)(1)))/(2(1))\\y=(-3+√(5))/(2)\\-------------------------\\y=(-3-√((3)^2-4(1)(1)))/(2(1))\\\\y=(-3-√(5))/(2)\\`

Your final answers are:

`y=-(3+√(5))/(2)` AND
`y=-(3-√(5))/(2)`