Question

complete the square
z^2=16z-64

Answer 1

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

Answer 2

can you see it now?

Answer 3

i got that part

Answer 4

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

Answer 5

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

Answer 6

Which means one solution for z, z=8.

Answer 7

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

Answer 8

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:\[(z-8)^2=7 \rightarrow z-8=\pm \sqrt{7} \rightarrow z=8 \pm \sqrt{7}\]

Answer 9

thank u

Answer 10

welcome :) hope you pass!