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Completing the square means changing the equation so it has a perfect square trinomial, (p-a)^2. (p-a)^2 = p^2 - 2ap + a^2. So in your equation, p^2 - 2ap is p^2 - 8p. So 2a = 8, so a=4. So +^2 would be +16. So you need to add 16 to each side of the equation (to keep the equation meaning the same thing). So change it to p^2-8p+16=0+16, or p^2-8p+16=16, or (p-4)^2=16. Take the square root of each side, so the absolute value of (p-4) equals 4, or p-4=+/-4, so p-4=4 and p-4=-4. Solve each of thoser 2 equations, so p=8,0.