# Complete the square

• Mar 9th 2008, 11:56 PM
stellina_91
Complete the square
Complete the square on:

x^2 - 8k

and

k^2 + 4k
• Mar 10th 2008, 12:01 AM
Moo
Hello,

Isn't it k^2 - 8k in the first one ?

You must associate these expressions with the formulas you should know :

(a-b)² = a² - 2ab + b²

(a+b)² = a² + 2ab + b²

So in each case, you'll got to find what is a. Then find 2ab. Hence, you got b, and you complete your expressions with b² ;)
• Mar 10th 2008, 04:59 AM
topsquark
Quote:

Originally Posted by stellina_91
Complete the square on:

x^2 - 8k

Let's demonstrate with the first one:
$k^2 - 8k$

We are comparing this to
$k^2 + 2bk + b^2 = (k + b)^2$

So by matching the coefficients of the linear (k) term we see that
$2b = -8 \implies b = -4$

Thus we need to add $b^2 = (-4^2) = 16$ to the expression. But we can't do that and not change the expression. So we have to be a bit clever about this and add $16 - 16 = 0$ to the expression. That way the value of the expression does not change.

So
$k^2 - 8k = k^2 - 8k + 16 - 16 = (k - 4)^2 - 16$

You do the second one.

-Dan