Let x be a positive number such that 2x^2=4x+9-2x+1. If x can be written in simplified form as (a + sqrt(b))/c such that a, b, and c are positive integers, what is a+b+c?
Rearrange as
2x^2 -2x = 10 divide through by 2
x^2 - 2x = 5 complete the square on x
x^2 - 2x + 1 = 5 + 1
(x - 1)^2 = 6 take the positive root
x - 1 = sqrt (6)
x = 1 + sqrt (6)
x = (1 + sqrt (6) ) / 1
a + b + c = 8
