The product of a number and 1 less than the number is 20. Find the number

Question

The number is __. (Use a comma to separate answers as needed.) 

Answer 1

Okay, if you know your basic multiplication table, then you know that 4 * 5 = 20 (similarly, -4 * -5 = 20 too), but let's solve this through algebraic methods:

x(x - 1) = 20

x² - x = 20

x² - x - 20 = 0

 

(x + m)(x + n) = 0

 

We know m and n need to answer to the following:

m + n = - 1

m * n = -20

That gives us:

4 - 5 = -1

4 * -5 = -20

 

(x + 4)(x - 5) = 0

So x + 4 = 0, and x - 5 = 0

Isolating x gives us the following possibilities:

x = -4, 5