A number is four times larger than the square of half the number

Step-by-step explanation:

Let the number = x

Read carefully the sentence part beginning with 4 times larger

4 * something

4 times larger than the square of 1/2 the number

4 * (x/2) ^2

4 * (x/2) ^2 = x

4*x^2/4 = x

x^2 = x be very careful how you handle this. It looks like 0 might be an answer, but it isn't. If you divide x on both sides and you allow 0, you will get 0 / 0 and that is undefined. You must exclude that possibility with some sort of statement.

x cannot be 0.

x^2/x = x/x

x = 1