The difference of a number and 24 is equal to twice the positive square root of the number. Find the number.
A) 36
B) 42
C) 38
D) 41
E) 39

Question

Quizplus · Accepted Answer

The equation based on the given statement is $x - 24 = 2\sqrt{x}$. Squaring both sides to eliminate the square root gives $(x - 24)^2 = 4x$. Expanding and simplifying, $x^2 - 48x + 576 = 4x$, which simplifies to $x^2 - 52x + 576 = 0$. Factoring or using the quadratic formula, we find $x = 36$ as the solution that makes sense in the context of the problem (since the square root of a number must be real and positive).

The Difference of a Number and 24 Is Equal to Twice