Hello from MrBillDoesMath!
Discussion:
The original equation is 16x^2 + 1 = 7x. Subtracting 7x from each side, and then dividing by 16, gives
x^2 - (7/16)x + 1/16 = 0
Recall that (x -a)^2 = x^2 -2ax + a^2 is the form of a perfect square. So dividing (7/16) by 2 gives 7/32 which is the quantity we need to square and add to make a perfect square:
x^2 - (7/16)x + (7/32)^2 - (7/32)^2 + 1/16 = 0
or
(x - 7/32)^2 = (7/32)^2 + 1/16
Final hint: (7/32)^2 + 1/16 = 113\1024
Hope this helps.
Regards, MrB
