Question

x2-6x+9=64

Answer 1

Factor x²-6x+9=64

x²-6x+9-64=0
x²-6x-55=0
the factors of 55 are 11 and 5
the difference of which is 6, so try
(x-11)(x+5)=0, and it works.
This the solutions of the equation are
{11,-5}
Check: (11^2-6*11+9=64, so 11 is good.
Check the same for -5.