Algebra Ages Question GCSE

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I need help to work out this algebra question.

Question: Ram's Daughter's Age in 3 years will be the square of her age 3 years ago. How old is she now?

What I did: algebraically: x+3 is daughters age in 3 years

x-3 age years ago

x+3 = (x-3)(x-3)

   x-3 = 0
   x=3

x = 3 so her age now is 3 years old?

On the mark scheme it said the answer was 6 but it didn't show the working so please can someone try this question and tell me what I did wrong.

Thank You and Help is Appreciated

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Your setup of

$$x + 3 = (x - 3)(x - 3)$$

is correct, but I have no idea how you concluded that $x - 3 = 0$ from this. I guess that you tried setting the factors on the right equal to zero, but there is no reason to here... their product is $x + 3$, not zero. Rather, expand and collect terms:

$$x^2 - 6x + 9 = x + 3 \iff x^2 - 7x + 6 = 0 \iff (x - 6)(x - 1) = 0.$$

So now it is valid to set each of the factors to zero, and so either $x = 6$ or $x = 1$. The latter solution doesn't make sense, so $x = 6$.