Question

The square of a positive number is 24 more than 5 times a number. What is the value of the number?

Answer 1

Answer: The positive number is
`8`.

Step-by-step explanation: Let, the positive number to find be
`x`. Then, its square will be
`x^(2)`. Sicne
`x^2` is
`24` more than
`5x`, so, while forming an algebraic equation from the given information, we will write

`x^(2) -24=5x\\\Rightarrow x^(2) -5x-24=0\\\Rightarrow x^(2) -8x+3x-24=0\\\Rightarrow x(x-8)+3(x-8)=0\\\Rightarrow (x-8)(x+3)=0,`

which gives

`x-8=0\Rightarrow x=8`

and

`x+3=0\Rightarrow x=-3.`

Since the given number is positive, so
`x=-3` cannot be true. Hence,
`x=8` is the solution.

Thus, the positive number is
`8`.

Answer 2

First, let's construct an algebraic equation to formally find the answer:

Let x represent (the value of) the unknown number.

x²= 5x + 24 --- This equation shows that the (positive) number's square equals 24 more than 5 times the number.

Now we can solve for x (the number):

x² = 5x + 24
x² - 5x - 24 = 0
(x + 3)(x - 8) = 0
x = -3, 8

Therefore, this means that x (the number ) can be either -3 OR 8. Both will satisfy the description.
Hope this helps!