how do I solve for X? 0=(X+6) sqrt (9-X^2)?

Answer 1

Are you sure you got everything here correct?

Because the way things are presented, if you could get (x+6) = 0 or sqrt (9-x^2) = 0 then the whole thing would be zero.

So the first part x + 6 = 0 gives x = -6

In the second part 9 - x^2 = 0 gives x = +/- 3

Hope this helps, I will check back later for additional comments.

Answer 2

If a*b = 0, then either a = 0 or b = 0 (or both). The only way to multiply 2 numbers and get 0 is for one (or both) to be zero. Therefore:

x+6 = 0 or 9-x^2 = 0

a) x + 6 = 0, x = -6

b) 9-x^2 = 0, x = -3 or 3

So your solution is x = -6, -3, or 3

Hope this helps! :)

Answer 3

One of your terms, x+6 or sqrt (9-x^2), must equal zero.

0 = n * m, n or m or both equal zero
where n=x + 6 and m=sqrt(9 - x^2)

solve for n=0
x + 6 =0
x = -6

solve for m=0
sqrt(9 - x^2) = 0
9 - x^2 = 0; squared both sides
9 = x^2
sqrt(9)= x
x = |3|; x equals 3 or -3

the valid answers for x are 3, -3 and -6