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The Square Root Trick

OK, here's the trick:

x^2

 We'll take the square root:  sqrt( x^2 )

  Squares and square roots undo each other... Right?

sqrt( 3^2 ) = sqrt( 9 ) = 3   Yep!

So,  sqrt( x^2 ) = x

Now, remember our equation rules -- whatever we do to one side, we have to do to the other.  So, we'll take the square root of both sides:

sqrt( x^2 ) = sqrt( 4 ) which gives x = 2

Uh oh... We only got one answer.  Hmm... We got two answers when we factored.

x = -2 or x = 2

Here's what you officially do to fix this problem:

x^2 = 4 gives sqrt( x^2 ) = +/- sqrt( 4 ) ... the plus or minus is very important! ... the equation gives x = +/- 2

{ -2 , 2 }