Question 666809: I have to backwards distribute this equation and I can't figure out if it's factorable.
4xsquared - 80 = 0
I have to somehow get it to be
(4x+____)(x-____) But I can't figure out what factors of 80 would also equal 0x.
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! You don't have a linear term in x so you don't need to do what your trying to do. Just recognize that you have the difference of two perfect squares or just do the following
(1) 4x^2 - 80 = 0
Now add 80 to each side and get
(2) 4x^2 = 80, now divide each side by 4 and get
(3) x^2 = 20, now take the square root of each side and get
(4) x = +/- sqrt(20) or
(5) x = +/- 2*sqrt(5)
If you want it in factored form, it is
(6) (x+2sqrt(5))*(x-2sqrt(5)) = 0, which is the same you would get using difference of two perfect squares.
Hint: Always remove all common factors before you begin a problem of this type. In your case, you could factor a 4 out of (1) and get x^2 - 20 = 0 to start with.
PS You can always use the quadratic factoring equation.
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