How do you solve the equation #3(x-2)^2-12=0#
Lets simplify this scary thing 1st
This qill be
so this is rewritten as
The zero rule here has to be either
Hence the roots of these equations are
Another path you could take to solving this equation would be to pull out a GCF. As you can see, all your terms on the left are divisible by 3. And since you just have 0 on the right, you can just divide everything by 3.
Then you get:
Now you could expand the binomial here, but since 4 is a perfect square, it's just much easier to move it over to the other side (add 4 to both sides), and then take the square root of both sides of the equation.
Make sure you pay attention to the fact that since you took a square root, it's plus OR minus 2, and not just 2
Now, just add 2 to both sides, and you're done.
Hope that helped :)