Question

How do you solve `(x+1)^2(x+2)=0`?

Answer 1

There are two solutions: `x_1 = -2 " and "x_2 = -1`.

Explanation:

`(x+1)^2(x+2)=0`
Therefore,
`(x+1)^2 = 0 " or " x+2=0`

So our first value of x is:
`x_1+2=0 -> x_1=-2`

The two other values can be solved for by rewriting.
`(x+1)^2 = 0-> (x+1)(x+1) =0`
Because this is a perfect square there is only one solution.
So, `x_2+1 = 0 -> x_2 = -1`.

Our solutions are, `x_1 = -2 " and "x_2 = -1`.