SOLUTION: The sum of five times a number and five times its square is 210. Determine the numbers

Question 925026: The sum of five times a number and five times its square is 210. Determine the numbers
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let n be the number we want.
Then we have
(1) 5n + 5n^2 = 210 or after dividing both sides by 5 we have
(2) n + n^2 = 42 or
(3) n^2 + n - 42 = 0
Now factor (3) and get
(4) (n+7)*(n-6) = 0, giving us the roots
(5) n = -7,6
Let's check the answers with (1).
Is (5*(-7) + 5*(-7)^2 = 210)?
Is (-35 + 5*49 = 210)?
Is (-35 + 245 = 210)?
Is (210 = 210)? Yes
Is (5*(6) + 5*(6)^2 = 210)?
Is (30 + 5*36 = 210)?
Is (30 + 180 = 210)?
Is (210 = 210)? Yes
Answer: The set {-7,6} satisfies the problem statement.
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