Question 620115
x^2 + 16 = 8x
First, we need to move everything to one side of the equation and set it equal to zero.

x^2 + 16 = 8x  Subtract 8x from both sides:
x^2 - 8x + 16 = 0  Now factor this.  We're looking for two factors of 16 whose difference is 8.  Hmm...  Are you sure you didn't copy the problem down wrong and it's 
x^2 + 16 = -8x (minus 8x)?  I bet it is, so I'm going to solve that instead:

x^2 + 16 = -8x  Add 8x to both sides 
x^2 + 8x + 16 = 0    
(x + ...)(x + ...) = 0  Now find two factors of 16 whose sum is 8.  That would be 4x4=16 since 4+4= 8
(x + 4) (x + 4) = 0
At least one of these factors needs to be zero for this to be true:
(x+4) = 0  |  (x+4) = 0
Subtract 4 from both sides:
x = -4

Checking:
x^2 + 16 = -8x
(-4)^2 + 16 = -8(-4)
16 + 16 = 32
32 = 32 Check!