complete the square / find the missing term
z^2 - 2z

Question

jadeishere · Answer

In order to use the "Complete the Square" it needs to be a perfect square trinomial, I believe....

melodyeason74 · Answer

the question says to simplify and write as integer or a fraction

jadeishere · Answer

Um, I'm confused, and I'm not sure I can help. I need to be able to see the entire question.. Sorry, maybe @alivejeremy can help:)

melodyeason74 · Answer

ah, that was the whole question... thanks anyway though

alivejeremy · Answer

There are no terms

melodyeason74 · Answer

$$z ^{2}-2z$$

alivejeremy · Answer

z(z−2)

melodyeason74 · Answer

$$z ^{2}-2z+?$$
this is what the question shows, all it says is find the missing term that complete the square, ​(Simplify your answer. Type an integer or a​ fraction.)

alivejeremy · Answer

=z^2−2z

alivejeremy · Answer

There shouldn't be nothing missing.

alivejeremy · Answer

Wait let me check again.

austin.l · Answer

$$z^2+2z+x=0$$

That seems like how I would start it, solve for it from there.

But I'm a bit rusty and I may be wrong.

austin.l · Answer

Correction,

$$z^2+2z-x=0$$

melodyeason74 · Answer

ok, i will try that

alivejeremy · Answer

Do you want us to find the degree ?

alivejeremy · Answer

Because you really can't simplify

alivejeremy · Answer

and there's really nothing missing.

alivejeremy · Answer

Unless you want us the find what make =z^2−2z
?

melodyeason74 · Answer

um... sure if thats how its supposed to be solved, i wrote exactly what was on my paper so i dont know

austin.l · Answer

I mean, to complete the square it is usually an expression set equal to 0. I'm not entirely sure how to tackle this to be honest.

Are  you sure that is the entire problem?

alivejeremy · Answer

(z-1)^2 - 1

melodyeason74 · Answer

im positive, that is why im so confused

welshfella · Answer

you can wrte it in the form 
(z - 1)^2  - 1

alivejeremy · Answer

What I was thinking ^

welshfella · Answer

the question is confusing

welshfella · Answer

maybe the missing term is -1 ???

abdullahm · Answer

a^2 + 2ab + b^2 = (a + b)^2

We want to find the term "b^2" and so we can reduce it into the form of (a + b)^2

The way to find b^2 is by taking 2ab dividing it by 2a and squaring it.

In our case we need to do $\Large \left(\frac{2z}{2z}\right)^2 = 1$

And that is our missing term.

austin.l · Answer

But that still doesn't alleviate the issue of us having to complete the square when all we have is an expression and not an equation.

Because if that expression was set equal to zero, I think I might do something along the lines of:

$$z(2+z)=0$$

abdullahm · Answer

Completing the square is a way of adding a term to be able to factor it into a perfect square trinomial.

welshfella · Answer

yea  I think abdullah is right 
the missing term is  + 1

that makes z^2 - 2z + 1 a perfect square

melodyeason74 · Answer

thanks y'all, sorry for the trouble

welshfella · Answer

there is no need to equate it to zero

austin.l · Answer

Oh my goodness, I was using a + instead of a - the entire time.

My way would have worked if I had had the signs correct.

welshfella · Answer

yw

austin.l · Answer

Long way around it, but good job @AbdullahM 

Take your filthy medal sir.

abdullahm · Answer

The last term in a perfect square trinomial will always be positive.

(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2