## anonymous 5 years ago complete the square z^2=16z-64

1. anonymous

try putting everything on one side. $z^2 -16z + 64 = 0$

2. anonymous

can you see it now?

3. anonymous

i got that part

4. anonymous

You need to add half of the coefficient of z and square it (do it to both sides).$z^2-16z=-64 \rightarrow z^2-16z+(-\frac{16}{2})^2=-64+(-\frac{16}{2})^2$

5. anonymous

$z^2-16z+(-8)^2=-64+(-8)^2$You can read off the left now as:$(z-8)^2$and the right is simply 0, so your equation becomes,$(z-8)^2=0$

6. anonymous

Which means one solution for z, z=8.

7. anonymous

its suppose to be two answers so would it be 8,-8??

8. anonymous

Well, not in this case, since the right-hand side ended up being zero. When you take the square root of both sides, z-8 = +/- 0 = 0 so z = 8. If you'd had, (z-8)^2 = 7, for example, THEN you'd have two solutions:$(z-8)^2=7 \rightarrow z-8=\pm \sqrt{7} \rightarrow z=8 \pm \sqrt{7}$

9. anonymous

thank u

10. anonymous

welcome :) hope you pass!