y = x^2 - 8x + 5 Put brackets around the first two terms.
y = (x^2 - 8x ) + 5 Add (8/2)^2 on the inside of the brackets. Translated into mathese that means take 1/2 of the linear term (8x), drop the x and square the rest
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(1/2 8)^2 = 4^2 = 16
y = (x^2 - 8x + 16) - 5 What you put inside the brackets, you must subtract outside the brackets.
y = (x^2 - 8x + 16) - 5 - 16 Combine like terms.
y = (x^2 - 8x + 16) - 21 Show what is inside the brackets as a square.
y = (x - 4)^2 - 21 <<<<<<<<< Answer.