Find the minmum value of x^2-4x+y^2+8y+20=?
we don’t know what it’s equal to, so we set it equal to ?, if you know that ? is, then input it
what we can do is try to convert it to a conic section
complete the squares

take 1/2 of linear coefient and square it and add negative and positive insde (linear is 1st degree)

factor perfect squares

we see this is the equation of a circle
in form
center is (h,k)
radius is r
so the lowest point is r  units down from (h,k), or the point (h,k-r)

we know that te equation is
center is (2,-4)
the minimum value, where the equation is equal to ?, is (2,-4-√?)
good luck, and may the force be with you