Question

`{x}^(2) + 4x - 8`

Can be written as

`{(x + p)}^(2) + q`
Find the values of p and q

Answer 1

Here you're being asked to "complete the square" of x^2 + 4x - 8.

1. Take half of the coefficient (4) of x and square it: Square 2: 2^2 = 4
2. Add this result to the given x^2 + 4x - 8, and then subtract the same:

x^2 + 4x - 8 + 4 - 4
3. Rewrite x^2 + 4x + 4 as a perfect square:
(x+2)^2 - 12
4. Identify p as being 2 and q as being -12.