Question

I need help completing the square, please =)

Answer 1

Only the solutions of g(x) will lead you safely across.

Answer 2

g(x) = x^2 + 6x + 3

Answer 3

do you know what a "perfect square trinomial" is?

Answer 4

Pretty much

Answer 5

Do I have to make it a perfect square trinomial?

Answer 6

\(\bf g(x) = x^2 + 6x + 3\implies g(x) = (x^2 + 6x) + 3\\ \quad \\
g(x) = (x^2 + 6x+{\color{red}{ \square }}^2) + 3\)

what do you think we need there to make a "perfect square trinomial"?

Answer 7

yes, "completing the square" really just means, "make it with a perfect square trinomial"

Answer 8

I believe you divide 6 by 2 then square it, so it would then be g(x) = (x^2 + 6x + 9) + 3?

Answer 9

And okay

Answer 10

yes... so we ADDED \(3^2\) so we also have to SUBTRACT \(3^2\) as well

recall, all we're doing is borrowing from Mr Zero, 0, so 9-9 = 0 and \(\bf x^2 + 6x + 3+0 \implies x^2 + 6x + 3\)

so \(\bf g(x) = x^2 + 6x + 3\implies g(x) = (x^2 + 6x) + 3\\ \quad \\
g(x) = (x^2 + 6x+{\color{red}{ 3 }}^2) + 3-{\color{red}{ 3 }}^2\)

Answer 11

\(\bf g(x) = (x^2 + 6x+{\color{red}{ 3 }}^2) + 3-{\color{red}{ 3 }}^2\implies g(x)=(x+3)^2-6\)

Answer 12

Thank you

Answer 13

@jdoe0001 , can you help me with one more?