Okay, Salome - you're almost right except for one thing: the last line. When x = 5, and x = -2, what you need to do is this: subtract 5 from the first one to be x-5 = 0. For the second one, you need to subtract -2 from the sex...oops I mean second one (hee hee hee) to be x -(-2) = 0, and remember that negative times negative is positive. That means x+2 = 0. Why all of this? Remember that rule - if ab = 0 then a = 0 or b = 0, or both? Check this out.
x - 5 = 0, or if a = x - 5, then a = 0
x + 2 = 0, or if b = x + 2, then b = 0,
Now, we know that 0 times 0 is 0...we can multiply x - 5 by x + 2, and get...
(x - 5)(x + 2) = 0, and voila (confetti falls from the sky)! And we have our equation! Don't believe me? Multiply it back using FOIL and you will get x squared minus 3x minus 10 = 0, and since 2 times zero is zero, we could multiply both sides by 2 to get the original problem.
Thank you for taking the time to answer!
However now I'm confused again.
Note: I could have stated that equation as a function, for it is one. Yeah, we have two different x values, but each x value will produce a distinct y, even though it could be the same y value. You can have that situation occur in a function. (For vectorspace: and I know that this function will not have an inverse.
Thank you for correcting me, as I didn't realize that the square root is DEFINED to be a function.)