Complete the square on:
x^2 - 8k
and
k^2 + 4k
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
Let's demonstrate with the first one:
$\displaystyle k^2 - 8k$
We are comparing this to
$\displaystyle k^2 + 2bk + b^2 = (k + b)^2$
So by matching the coefficients of the linear (k) term we see that
$\displaystyle 2b = -8 \implies b = -4$
Thus we need to add $\displaystyle b^2 = (-4^2) = 16$ 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 $\displaystyle 16 - 16 = 0$ to the expression. That way the value of the expression does not change.
So
$\displaystyle k^2 - 8k = k^2 - 8k + 16 - 16 = (k - 4)^2 - 16$
You do the second one.
-Dan