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