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

Question

This is a quadratic. Please help, as I do not know the method for the a(x-p)^2=y form. Again, using the square root method.

Answer 1

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.