If 6 is a root of the equation x^2-8x+k=0, find the value of k.
To find the value of k, we can use the fact that if 6 is a root of the equation x^2 - 8x + k = 0, it means that when we substitute x = 6 into the equation, the equation will be satisfied, or in other words, the equation will equal to zero.
So, let's substitute x = 6 into the equation:
(6)^2 - 8(6) + k = 0
36 - 48 + k = 0
-12 + k = 0
To isolate k, we move -12 to the other side of the equation by adding 12 to both sides:
k = 12
Therefore, the value of k is 12.