Question

How do you solve `x^2+15x=0`?

Answer 1

`color(blue)(x=0)` or `color(blue)(x=-15)`

Explanation:

Factoring `x^2+15x=0`
gives
`color(white)("XX")x(x+15)=0`

which implies
either
`color(white)("XX")x=0`
or
`color(white)("XX")(x+15=0)`
`color(white)("XXXXX")rarr x=-15`

Answer 2

`x= 0, or x = -15`

Explanation:

The first approach is always to try and factorise the quadratic. Although this is not a trinomial, there is a common factor.

`x(x+15)=0`

Because the product is 0, one of the two factors must be equal to 0.

Either `x = 0, or x+ 15 =0," in which case " x = -15`

This gives two solutions, exactly what we expect with a quadratic.