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How to solve 3(x-4)^2=75 with the square root method

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1 Answer

Hi Sam,
 
With the square root method, we need to get the equation in the form of
 
    something squared = something else
 
and then take the square root of each side.
 
So, first let's divide each side of your equation by 3, to get
 
    (x-4)^2 = 25
 
Now we can take the square root of each side, and get
 
    (x-4) = 5  and  (x-4) = -5
 
Remember, 5*5=25, but also -5 * -5 = 25, so taking the square root gives us two solutions. Now we solve each of our equations
 
    (x-4) = 5 --> x = 9
    (x-4) = -5 --> x = -1
 
Our two answers are thus x=9 and x=-1. I leave it to you to insert these values back into the original equation and make sure I got it ok! Always double check your work.