+1206 Find all numbers such that the square of the number is 48 more than double the number. If you find more than one, then list all the numbers you find in increasing order, separated by commas.
Solve for x:
x^2 = 2 x + 48
Subtract 2 x + 48 from both sides:
x^2 - 2 x - 48 = 0
The left hand side factors into a product with two terms:
(x - 8) (x + 6) = 0
Split into two equations:
x - 8 = 0 or x + 6 = 0
Add 8 to both sides:
x = 8 or x + 6 = 0
Subtract 6 from both sides:
x = 8 or x = -6
