Let \(x\) be a positive number such that \(2x^2 = 4x + 9.\) If \(x\) can be written in simplified form as \(\dfrac{a + \sqrt{b}}{c}\) such that a, b, and c are positive integers, what is \(a + b + c\)?
Rearrange as
2x^2 - 4x - 9 = 0
x = 4 + sqrt [ 4^2 - 4 * 2 * - 9 ]
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2 * 2
4 + sqrt [ 88]
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4
4 + 2sqrt (22)
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2 + sqrt (22)
2
a = 2 b = 22 c = 2
Sum = 26
