SOLUTION: We have been working on factoring trinomials and the problem I don't know how to solve is (x^2+4x-4)^2=64. I think what we're supposed to do is divide the exponent off both sides b
Question 354730: We have been working on factoring trinomials and the problem I don't know how to solve is (x^2+4x-4)^2=64. I think what we're supposed to do is divide the exponent off both sides but I'm not sure. Were I get stuck is you're left with x^2+4x-4 on one side and that doesn't facter into two binomials. HELP ME! Found 2 solutions by scott8148, Edwin McCravy:Answer by scott8148(6628) (Show Source):
We use the principle of square roots:
Take away the square on the right, take ± square roots of the right side
Make two equations, one with the + and one with the -
and
Solving the first one
Get 0 on the right:
Factor the left side by thinking of two whole numbers which
have product 12 and difference 4. They are 6 and 2. So
we write
Then we put in the signs so that if we were to FOIL it out
we would get the middle term in the middle.
Then we use the zero-factor principle:
set each factor = 0
gives solution gives solution
-------------------
Solving the second one
Get 0 on the right:
Factor the left side by thinking of two whole numbers which
have product 4 and sum 4. They are 2 and 2. So
we write
Then we put in the signs so that if we were to FOIL it out
we would get the middle term in the middle.
Then we use the zero-factor principle:
set each factor = 0
gives solution
The second factor is the same, so we do not get an additional solution.
Checking in the original equation:
Checking
Checking
Checking
They are all solutions.
Edwin