Solve using factoring

Question

2x²-x=3

Answer 1

Hello Amanda!

 

To start off, let's get this into an easier format by making everything equal to 0:

 

2x²-x-3=0

 

(All I did here was subtract 3 from both sides :) )

 

Next, we have to ask a few questions like we always do with factoring.  What, when added, (and with one of the two digits multiplied by 2) is equal to -1 and when multiplied is equal to -3?

 

Well, there are only two possibilities because the only factors of -3 would be either 1 and -3 or -1 and 3!

 

Using this, we need to find out how to get -1 by multiplying one of the two factors by 2 and adding it to the other.

 

-3+2(1)=-1

2(-3)+1=-5

3+2(-1)=1

2(3)-1=5

 

Out of our four possibilities, we are left with -3 and 1 being correct with 1 being the factor that is multiplied by two.  So our factorization would be:

 

(x+1)(2x-3) = 0

 

Now simply solve for x!

 

x = -1

and

x = 3/2

 

And we're done!