You and your friend are playing a number-guessing game. You ask your friend to think of a positive n

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen?

Let n be our original number.

Square the number means we raise n to the power of 2:
n^2

Multiply the result by 2:
2n^2

And then add three:
2n^2 + 3

If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53:
2n^2 + 3 = 53

To solve for n, we subtract 3 from each side, to isolate the n term:
2n^2 + 3 - 3 = 53 - 3

Cancel the 3's on the left side, and we get:
2n^2 = 50

Divide each side of the equation by 2:
2n^2/2 = 50/2

Cancel the 2's, we get:
n^2 = 25

Take the square root of 25
n = +-sqrt(25)
n = +-5

We are told the number is positive, so we discard the negative square root and get:
n = 5