If the square of a positive integer is added to 5 times the integer, the result is 36

Question

 If the square of a positive integer is added to 5 times the integer, the result is 36 

Answer 1

Let n bet the integer and n > 0.

 

Then n² + 5n = 36 => n² + 5n - 36 = 0

                                (n + 9)(n - 4) = 0

 

Then n = 4, since the intege4 is positive.

Answer 2

Here's what we know:

x² + 5x = 36 (the square of a number plus 5 times the number is 36)

Subtract 36 from both sides:

x² + 5x - 36 = 0

We now have a quadratic, which means we have the following:

(x + m) (x + n) = 0

To solve we need to find the following:

m * n = -36

m + n = 5

 

9 * 4 = 36

9 - 4 = 5

(x + 9)(x - 4) = 0

x = -9, 4

Since the question asks for a positive integer, we can throw away the -9, leaving us with 4.

 

Check:

4² + 5 * 4 = 36

16 + 20 = 36

36 = 36