The roots of the equation 2x^2 - 5x - 4 = 0 can be written in the form x = (m±sqrt n)/p, where m, n, and p are positive integers with a greatest common divisor of 1. What is the value of n?
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2x^2 -5x - 4 = 0 divide through by 2
x^2 - 5/2 x - 2 = 0 add 2 to both sides
x^2 - 5/2 x = 2 take 1/2 of 5/2 = 5/4.....square it = 25/16...add to both sides
x^2 -5/2 x + 25/16 = 2 + 25/16 simplify both sides
(x - 5/4)^2 = 57/16 take both rots
x - 5/4 = ±√57 / 4 add 5/4 to both sides
x = [ ±√57 + 5 ] / 4
So...n = 57