Question

Need help with completing the square, please =) (easy, just need an explanation)

Answer 1

Justify if completing the square is a good method for solving when the Discriminant is negative. Use any of your three functions as an example and respond in complete sentences.

f(x) = x^2 - 4
g(x) = x^2 + 6x + 3
h(x) = x^2 + 2

Answer 2

this is for the second one
take half the middle term 3
then x^2+6x+3=(x+3)^2+3-3^2 = (x+3)^2+3-9 = (x+3)^2-6
so all I did was put half the middle term in the binomial (x+3), then square that (x+3)^2, then we still have the original 3 on the end (x+3)^2+3 and we
subtract half the original middle term squared (x+3)^2+3-3^2

Answer 3

now solving is easy\[(x+3)^2-6=0\\(x+3)^2=6\\x+3=\pm \sqrt{6}\\x=\pm\sqrt{6}-3\]

Answer 4

Okay, makes sense. It says to justify if the discriminant is negative, and if I remember correctly, the discriminant was 24.

Answer 5

hmm, well the discriminant is not negative, and it works, and if the disc was negative then we would just have square root of negative number and thus our solutions would be complex. Have you heard about imaginary numbers?

Answer 6

Yeah, not very good with them, but I've dealt with them a little haha

Answer 7

hmm, so completing the square is a good method for every case, so im confused by the question

Answer 8

with another example,
x^2+2
x^2 = -2
x = +-sqrt(-2) = +-sqrt(2)*i

Answer 9

Okay

Answer 10

Now what?