X^2 = 9x

[BK87]

If you are given the statement x^2 = 9x. How come you cannot solve as follows:

X^2 = 9x
(x)(x) = 9x
x = 9

What is wrong with doing this?

Why do you have to subtract 9x from the right and set x^2 - 9x equal to 0?

[PetriF258]

Hi BK 87

Just my opinion. If you do it the way you suggested, you get one answer, i.e. x = 9. You can test it and it works, 9^2 = 9(9).

But, that is not the only possible answer. What if x = 0? Let's test it: 0^2 = 9(0). Therefore, x has two possible solutions, 9 and 0. Through changing the equation we get x^2 - 9x = 0 -->
x(x-9) = 0, therefore x = 0 or x = 9.

Bottom line: you are not allowed to divide by x as x could equal 0, and anything divided by zero is not allowed (I think it's called undefined or something, not sure)

[RonPurewal]

H
Bottom line: you are not allowed to divide by x as x could equal 0, and anything divided by zero is not allowed

^^ that.