Solve the equation

Question

I'm in a section about factoring/radicals etc. and I got stuck on questions like "solve the equation __z=__z² 

I know you take one to the other side to get 0 on the other, but how do you find z? For example, 9z=-10z, I brought 9 over to the right side so 0=-10z-9z and did 0=z(-10z-19z) but I dunno whats next. 

 

Answer 1

I can't follow your example, and what you are asking.  But let me give you a few scenarios that might be close.

 

First, if you have something like 9z=-10z, as you wrote at one point.  

 

9z=-10z

-19z=0 (subtract 9z from both sides, as you've done)

z=0 (divide both sides by -19)

 

Later you throw a z² in there, so I'm not sure what you are actually asking, but maybe something like the following?  If this doesn't answer your question, please post a specific problem.

 

9z=18z²

0=18z²-9z (subtract 9z from both sides)

0=9z(2z-1) (factor out the common 9z)

 

Since these two pieces are MULTIPLIED together, the left side will be 0 if EITHER piece on the right equals 0.  So from here on out, you are looking at 2 possible solutions.

 

Solution 1

9z=0

z=0 (divide both sides by 9)

 

Solution 2

2z-1=0

2z=1

z=1/2

 

So for this problem, z could be either 0 OR 1/2

 

If you have a third term, you are looking at a slightly different type of factoring.