What value of $k$ will make $4x^2 - 20x + k$ the square of a binomial?

k = 25

Step-by-step explanation:

(2x - sqrt (k)) ^2 Expand this as a binomial

4x^2 - 4x*sqrt (k) + k The middle term must be - 20x Solve for k so it is

-4xsqrt (k) = - 20x Divide by - 4x

sqrt (k) = - 20x/-4x Do the division

sqrt (k) = 5 Square both sides

k = 25