Question

Complete the square then rewrite as a perfect square.

1. z^2 - 19z + ? = 0

Answer 1

Ok so the original equation is this:
Z^2-19z+0=0

So to complete the square, what we will do is take half of (-19), which is 9.5.
Now we will square 9.5, which is 90.25
Now whatever we do inside the parentheses, we do the opposite on then outside, which is -90.25

In the final form, it would be
(z-9.5)^2 = 90.25
or
(z-9.5)^2 - 90.25 = 0

Answer 2

Hope this helped :)

Answer 3

Wait how did you get the final form? I'm confused on that part

Answer 4

Ok so the final form is simply written as the variable (plus or minus) half of the original term, in this case it was half of -19, which was -9.5, which equals. This gives the equation (z-9.5)^2, because if you square this you get z^2 -19 +90.25, which is the the full polynomial. Does this help clarify?