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!