The solutions of x(3x-7) = -3 + 2x may be expressed in the form m + sqrt n / p and m - sqrt n / p , where m, n, and p have a greatest common divisor of 1. Find m+n+p.
x(3x - 7) = -3 + 2x
3x^2 - 7x = -3 + 2x rearrange as
3x^2 - 9x = -3 divide through by 3
x^2 - 3x = - 1 complete the square on x
x^2 -3x + 9/4 = -1 + 9/4
(x - 3/2)^2 = 5/4 take both roots
x - 3/2 = ± √5/2
x = 3/2 ± √5/2
m= 3 n = 5 p = 2
m + n + p = 10
