Questions about the world of GRE Math from other sources and general math related questions.
flaviaq
Course Students
 
Posts: 1
Joined: Tue Aug 27, 2013 3:46 am
 

how to isolate a variable

by flaviaq Thu Nov 14, 2013 8:42 pm

how do you solve

a2/2 + a/2 = 6

a squared over two plus a over 2 equals 6 , I just cant do it !
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: how to isolate a variable

by tommywallach Fri Nov 15, 2013 6:27 pm

Hey Flavia,

Glad to help! Just so you know, we use the ^ symbol to do exponents (just so you don't have to type it out like that next time!).

a^2/2 + a/2 = 6

All we have to do is multiply everything by 2. Usually, when you're doing algebra, a good start is to get rid of denominators.

a^2 + a = 12

Now we can see this will be a quadratic (if you don't know what that is, time to hit the books!). Always set a quadratic equal to zero, in this case, by subtracting 12 from both sides.

a^2 + a - 12 = 0

In a quadratic, we solve by finding two numbers that multiply to the constant (-12, in this case) and sum to the coefficient on a (the invisible 1, in this case). This two numbers here would be -3 and 4, which we put in parentheses like so:

(a + 4) (a - 3) = 0

Our two solutions are going to be -4 and 3.

Hope that helps!

-t