Find all numbers such that the square of the number is 48 more than triple the number. If you find more than one, then list all the numbers you find in increasing order, separated by commas.
Solve for a:
a^2 = 3 a + 48
Subtract 3 a + 48 from both sides:
a^2 - 3 a - 48 = 0
Add 48 to both sides:
a^2 - 3 a = 48
Add 9/4 to both sides:
a^2 - 3 a + 9/4 = 201/4
Write the left hand side as a square:
(a - 3/2)^2 = 201/4
Take the square root of both sides:
a - 3/2 = sqrt(201)/2 or a - 3/2 = -sqrt(201)/2
Add 3/2 to both sides:
a = 3/2 + sqrt(201)/2 or a - 3/2 = -sqrt(201)/2
Add 3/2 to both sides:
a = 3/2 + sqrt(201)/2 or a = 3/2 - sqrt(201)/2, OR:
a =~ 8.5887 and a=~ -5.5887
