x2 + 8x + 16 = 0
This quadratic equation can be factored as (x+4)(x+4) = 0. This means that both x+4 and x+4 must equal zero in order for the entire equation to equal zero. Therefore, the solution is x = -4, and this value must be repeated twice since the factors are the same.
To solve the quadratic equation x^2 + 8x + 16 = 0, we can either use factoring, completing the square, or the quadratic formula. In this case, factoring and completing the square are the easiest methods:
Factoring:
(x + 4)(x + 4) = 0
So, x = -4 (only one solution since both factors are the same)
Completing the square:
x^2 + 8x + 16 = (x + 4)^2
This tells us that x + 4 = 0
So, x = -4 (the same solution as from factoring)
Thus, the solution to the quadratic equation x^2 + 8x + 16 = 0 is x = -4.