Question

How do you solve `v^ { 2} + 34v = 0`?

Answer 1

Factorization.

Explanation:

We can factor out a `v` from the given equation, doing this we get: `v * (v+34) = 0`

Now since two terms multiply to give us `0`, this means that one of them must be zero, so if the first term is `0` then `v = 0`, if the second term is `0`, then `v = -34`

So the solutions are `v = 0, v = -34`

Answer 2

`v= 0 or -34`

Explanation:

First off, identify that this is a quadratic equation, because the highest power of `v` is 2 (ie. `v^color(red)2`)

This means the solution has 2 answers.

Start by factoring out the `v`

`v (v+34)=0`

Now, this equation shows that either `v` or `(v+34)` is equal to zero.

`v = 0` or `v+34=0`

`v=-34`

Thus, `v = 0 or -34`

If you want to check your answers, substitute the `v` values back into the equation.

When `v=0,`

`0^2+34(0) = 0` (`v=0` is correct)

When `v=-34`,

`(-34)^2+34(-34)=0`
`1156-1156=0` (`v=-34` is correct)

Thus, `0` and `-34` are the 2 solutions that were mentioned at the start.