How find the values of x when x^2+8x+16=0?

We can find the values of x for this equation in several ways, we can either use the quadratic formula, complete the square, or see if the equation will factorise. For x^2+8x+16, we will first see whether we can factorise it. This means that first of all, we need to find two numbers that add to make 8, but multiply to make 16. In most cases it is useful to write out the factors of both these numbers. For 8 we have the factors: 1, 2, 4, 8. And for 16 we have the factors: 1, 2, 4, 8, 16. So from these we can see that 4 and 4 add to make 8 and multiply to make 16. This means that we can now factorise our equation. Factorising is essentially the opposite to expanding brackets, which means that will, in this case end up with something that looks like (?x+?)(?x+?)=0. Because we don't have anything in front of x^2, the question marks in front of the x's in the brackets will both be 1, and since we worked out that 4 and 4 will add to make 8, but multiply to make 16, we have: (x+4)(x+4)=0 which is the same as (x+4)^2=0. We can now square root both sides to give: x+4=0. Now subtracting 4 from both sides gives x=-4. This means that for x^2+8x+16=0 we have found that x=-4.