Question

Solve x2 + 4x – 12 = 0 by completing the square. Show your work for full credit.

Answer 1

it would be nice to add some useful form of zero to this thing to change the form, and not the value

Answer 2

x2 + 4x + (0)– 12 = 0

x2 + 4x + (n^2 - n^2)– 12 = 0

(x2 + 4x + n^2) - n^2– 12 = 0

(x2 + 4x + n^2) = n^2 + 12

the issue being, what is a good value for n such that the left side is a perfect (or complete) square?

Answer 3

nah, same generic variable would have been fine :)

a perfect square is of the form: (x+n)^2

(x+n)^2 = (x+n) (x+n)
= x^2 +2n x + n^2

there, now we have something to compare with

x^2 + 4 x + n^2
x^2 + 2n x + n^2

so, what is the value of n if: 2n = 4?