Write (x^2-12x+20) in completed square form.

Correct answer: ((x-6)^2-16)

The direct answer is A: \((x-6)^2-16\). Completing the square means creating a perfect square from the first two terms and adjusting the constant term. Half of the coefficient of x in \(x^2-12x\) is \(-6\), whose square is 36. Add and subtract 36: \(x^2-12x+20=x^2-12x+36-36+20=(x-6)^2-16\). Option A is correct. Option B, \((x+6)^2-16\), expands to \(x^2+12x+20\), so the middle sign is wrong. Option C, \((x-12)^2+20\), uses 12 instead of half of 12; it gives the wrong middle term and constant. Option D, \((x-6)^2+16\), expands to \(x^2-12x+52\), so the final constant is too large. The key is to add and subtract the same number, so the value does not change. Take half the middle coefficient, square it, and compensate outside the square.