Question

How do you find the solution to the quadratic equation `2(x^2 - 5)^2 - 13 (x^2 - 5) + 20 = 0`?

Answer 1

Let `p=(x^2-5)`
and solve
`2p^2 - 13p +20 = 0`
Then for each solution (in terms of `p`)
solve for `x`

`2p^2 - 13p +20 = 0`
`rarr (p-4)(2p-5) = 0`
`rarr p=4 " or " p = 5/2`

If `p=4`
`x^2-5 = 4`
`rarr x=+3 " or " x=-3`

If `p=5/2`
`x^2-5 = 5/2`
`rarr x=+15/2 = +7 1/2 " or " x=-15/2 = -7 1/2`

So
`x epsilon {-7 1/2, -3, +3, +7 1/2}`