Expert: Bobby Soltani - 8/11/2004

Question
   Hi Bobby.  How are you doing today?  Hope all is well.  This square root method thing is driving me crazy.  I was up till 3am last night.  Can you help me with these problems?

1.  x2 - 16 = 0

2.  (3x - 2)2 = 49

Answer
Hi Damon,

I'd be glad to help.

1. x^2 - 16 = 0
we want to sovle for x so we will try to manipulate the equation until it looks like x = something.  First we will add 16 to both sides.
x^2 = 16
now we have x^2 on the left.  Since we want only x, we take the square root of both sides.
x = 4 or -4
4 is the square root of 16.  You can check by saying 4^2 = 4*4 = 16.  We have to include -4 as well because when you square a negative number you get a positive number.  So, for
x^2 = 16, -4 will work also.  Let's try it.

(-4)^2 = 16
=(-4)*(-4) = 16
16 = 16

It works.

2. (3x-2)^2 = 49
take the square root of both sides
(3x-2) = 7 or -7
Let's break it in to two equations and solve both of them

First, (3x-2) = 7
add two
3x = 9
divide by three
x = 3

Second, (3x-2) = -7
add two
3x = -5
divide by three
x = -5/3

So the answer would be x = 3 or x = -5/3.

You can check it by plugging those back into the original equation.

Good Luck.

Bobby