Problem: find the number
the square of a positive number decreased by four times the number is 12
x^2 - 4x = 12
x^2 - 4x - 12 = 0
(x - 6)(x + 2) = 0
So, either (x - 6) = 0, or (x + 2) = 0, or both equal zero.
x - 6 = 0
x = 6
x + 2 = 0
x = -2
Check the answers.
x^2 - 4x = 12
6^2 - 4(6) = 12
36 - 24 = 12
12 = 12
x^2 - 4x = 12
(-2)^2 - 4(-2) = 12
4 + 8 = 12
12 = 12
Answer: x = 6, and x = -2