Can you help explain how I can simplify/find an equivalent expression to x^2 - 8x + 5

Question

The question says, "Which of the following is equivalent to the expression above?" with the expression being x^2 - 8x + 5

The answer is (x - 4)^2 - 11 but I don't understand how I can get to that answer/ I don't know the steps to get to that answer. Can you please explain and/or help?

Answer 1

x^2-8x +5 complete the square,

take half the x coefficient and square it, then add and subtract it

half of -8 = -4, square -4 to get 16. add 16 and subtract 16

adding and subtracting the same number, keeps the expression equivalent

x^2 -8x +16 + 5 -16

= x^2 -8x +16 -11

= (x-4)^2 -11

(x-4)^2 = x^2 -8x + 16