Let x be the positive number such that 2x^2=4x+9
If x can be written in simplified form as a+√bc such that a, b, and c are positive integers, what is a+b+c?
2x2=4x+9
2x2−9=4x
2x2−4x−9=0
x1,2=−(−4)±√(−4)2−4⋅2(−9)2⋅2
x1,2=−(−4)±2√222⋅2
x1=−(−4)+2√222⋅2,x2=−(−4)−2√222⋅2
x=2+√222,x=2−√222
In this case, it is
x=2+√222
2+22+2=26
so 26 is your answer!