What is the Integer?

Question

Twice the square of a positive integer is 12 less than 10 times that integer. What is the integer?

Answer 1

2x^2 +12 = 10x

2x^2 - 10x + 12 = 0

x^2 - 5x + 6 = 0

(x-3)(x-2) = 0

x = 2,3

 

 

Answer 2

 

If n is the integer in question,  twice the square is 2n²

"12 less than 10 times that integer"   is  nothing more than  10n-12

 

The keyword "is" is the cue for "=" : 

 

                2n² = 10n - 12

 

2n² - 10n + 12 = 0     (moved everything to one side)

(2n - 6)(n - 2) = 0      (factored)

 

 

2n-6 = 0   —>  n=3

n-2 = 0     —>  n=2

 

Both of these answers work.