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.