y2-2py+ =15p2: Then, Divide the coefficient of y in the middle term (-2p) by 2 (that will be -1p) and square it. You get 1p2 or p2 (they are the same). That is completing the square.
p2 is your new third term.
y2-2py+p2=15p2+p2 <-- be sure to add p2 to both sides
y2-2py+p2=16p2: Factor to find the square root for both sides
(y-p)2 = ±4p2:
y-p= +4p and y-p = -4p
So. y = 5p and y = -3p
2. x2-3kx+2k2 = 0
x2-3kx+ = -2k2 : Divide the number in the middle term (-3) by 2. That is (-3/2) and square it...9/4 k2
x2-3kx+9/4 k2= 1/4 k2 <-- Add 9/4 k2 to both sides
(x-3/2 k)2 = ±1/2 k
x-3/2 k = 1/2 k and x-3/2 k = -1/2 k
So, x = 2k and x = k