Question

Question #72d7d

Answer 1

`x=-3±sqrt14`

Explanation:

Find two numbers that multiply to negative 5 and add to 6.

Since `5` is a prime number, its only factors are `5 and 1`.

If one of these is negative then they'll multiply to `-5`. Unfortunately, `-5 xx 1 = 5` but `-5+1=-4` and not `6`

Also `5 and -1` add to `4` and not `6`... this means it can't be factorised so we will have to use completing the square or the quadratic formula.

First, divide 6 by two and square it with `x`:

`(x+3)^2` this would expand to `x^2+6x+9` which is right except for the `9` - we need `-5` so we subtract `14`.

`(x+3)^2-14=0`

now solve for `x`:
`(x+3)^2=14`
`x+3=±sqrt14`
`x=-3±sqrt14`