Question

For the equation `x(2x – 1) = 2016`, how to find the values of x?

Answer 1

`x = 32 or x=-31.5`

Explanation:

`x(2x-1)=2016" "larr` multiply out the bracket

`2x^2 -x -2016=0" "larr` it is a quadratic, make equal to `0`

The factors should be easy to find because they only differ by `1`.
We can use the square root to find them, because the square roots are 2 factors which are the same, so our required factors will be very close.

`2 xx 2016 =4032`

`sqrt4032 = 63.498....`

Try numbers close: `63xx64 = 4032`

Use this to find the factors of `2 and 2016` to make `63 and 64`

`2 and 2016`
`darr" "darr`

`2" "+63" "rarr 1 xx +63 = +63`
`1" "-32" "rarr 2 xx -32 = -ul64`
`color(white)(wwwwww.wwwww.wwwwwwww)-1`

`(2x+63)(x-32)=0`

Let each factor be equal to `0` and solve for `x`

`2x+63 = 0 " "rarr x = -63/2 = -31.5`

`x-32 = 0" "rarr x = 32`