There are two distinct solutions $x$ to the equation $18+5x^2=20x$. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?
+128474 18 + 5x^2 = 20x rewrite as
5x^2 - 20x + 18 = 0
Complete the square on x
5 ( x^2 - 4x + 18/5) = 0
5 ( x^2 - 4x + 4 + 18/5 - 4) = 0
5 ( (x - 2)^2 + 18/5 - 20/5 ) = 0
5( (x - 2)^2 - 2/5) = 0
(x - 2)^2 - 2/5 = 0
(x - 2) ^2 = 2/5 take both roots
x -2 = ±√(2/5)
x = 2 ±√(2/5)
This evaluates to x ≈ 1.3675 x ≈ 2.6325
The desired rounding produces 1 and 3 and their product is 3
