Question

N^2 = 6n+c , Solve for c to make perfect square

Answer 1

Cute

Answer 2

Why is there an \(=\) sign?

Answer 3

Should it be \(+\) or \(-\)?

Answer 4

Im not sure..
Whats cute about this..

Answer 5

Is it really an \(=\)?

Answer 6

Yes.

Answer 7

Then I think the first thing you have to do is move it all to one side.

Answer 8

Its a quadratic equation..

Answer 9

\[
n^2-6n-c=0
\]

Answer 10

In general, we would observe that \[
(n+a)^2 = n^2+an+an+a^2 = n^2+2an+a^2
\]

Answer 11

If we set them equal, then: \[
n^2+2an+a^2=n^2-6n-c
\]And if we set the coefficients equal, we get: \[
2a=-6\\
a^2=-c
\]

Answer 12

When we solve the first equation\[
2a=-6\implies a=-6/2=-3
\]We can put it into the second equation: \[
(-3)^2 = -c\implies 9=-c\implies c=-9
\]

Answer 13

So we would say: \[
\big (n-3\big)^2 = n^2-6n+9
\]And that \(c=-9\).

Answer 14

I think this question is difficult for no reason, but thank you.

Answer 15

Usually they have you memorize some formula

Answer 16

Like \(b/2\) or something