Help with the following complete the square equation...

Answer:  D) Add 64 to both sides

Why do this?

Because we want to be able to factor the left hand side into the form p^2, where p is some algebraic expression. This will help us ultimately solve for x.

Currently, the left hand side is x^2+16x which does factor to x(x+16), but that isn't in the form p^2. We want something like (x+1)^2 or (x+2)^2. The general form is (x+k)^2 where k is some fixed constant.

Let's expand out (x+k)^2 using the FOIL rule and we get x^2+2kx+k^2

The x coefficient is 2k. If we cut that in half, we get k. Squaring that result leads to k^2.

So we have this order: 2k cuts in half to k then square it to get k^2

For x^2+16x, we have the x coefficient as 16. That cuts in half to 8, then that squares to 64. We add 64 to both sides

Note how

x^2+16x = 9

x^2 + 16x + 64 = 9+64

(x+8)^2 = 73

From here, we apply the square root to both sides and then subtract 8 from both sides to fully isolate x. You would get two different solutions.

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I recommend you use the FOIL rule to confirm that (x+8)^2 expands out to x^2+16x+64, to help check your work.