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We've been solving nice guys like

x^2 - 3x - 18 = 0
Notice that it's already set equal to 0.

So, what if the problem starts out like this?

x^2 - 3x = 18

Can we just factor and do the blob thing?

x ( x - 3 ) = 18

So x = 18 or x - 3 = 18 which gives x = 21

Are these the answers?  Check them!

x = 18: x^2 - 3x - 18 = 0 which gives ( 18 )^2 - 3 ( 18 ) - 18 = 0 which gives 324 - 54 - 18 = 0 ... No way!

Why didn't this work?

Think about our main idea"

If a * b = 0 , then a = 0 or b = 0

IT MAKES SENSE!

But, THIS is what we tried:

If a * b = 18 , then a = 18 or b = 18

WE CANNOT SAY THIS!

Uh.... What about

3 * 6 = 18 or 2 * 9 = 18 ?

There are a ton of things a and b can be other than 18.

So, when you start with something like

x^2 - 3x = 18

ALWAYS SET IT  = 0  FIRST. 
ALWAYS!

x^2 - 3x - 18 = 0

Finish it!


YOUR TURN:

Solve  x^2 + 7x = 170