if I multiply a number by 10 and subtract 9, I get the square of the number. What could the number be?

Question

im having trouble putting it into an equation.

Answer 1

n = the number

10n - 9 = n²

0 = n² - 10n + 9

0 = (n - 1)(n - 9)

 

{ 1, 9 }

 

The number could be either 1 or 9. 

 

 

Answer 2

Let x = the number.  If I multiply a number by 10 and subtract 9, I get the square of the number:

 

10x - 9 = x²

0 = x² - 10x + 9

 

Factors to:

 

0 = (x-9)(x-1)

x = 9 and 1

 

Check:

10(9) - 9 = 9²

90 - 9 = 81

81 = 81    Check!

 

10(1) - 9 = 1²

1 = 1    Check!