Question

Seventy-five times an integer, minus 36, equals 21 times the square of the integer. Which equation could be used to solve for the unknown integer?

Answer 1

The answer would be 21x2 − 75x + 36 = 0

Explanation:

21x2 − 75x + 36

75x − 36 = 21x2

21x2 + 75x − 36 = 0

3(x + 4)(7x − 3) = 0

x = −4 or x = 3/7

Thus, the unknown negative integer is −4.

Answer 2

75n-36=21n^2 rearrange so we have an equation equal to zero...

21n^2-75n+36=0 divide whole equation by 3

7n^2-25n+12=0 now factor...

7n^2-21n-4n+12=0

7n(n-3)-4(n-3)=0

(7n-4)(n-3)=0

Since this is an integer 4/7 is extraneous.

The integer value is 3