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show the equation (x-4)^2=9 can be solved both by factoring and extracting the root

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Jeonelvieviz
x²-8x+7=0
x²-8x=-7
x²-8x+[1/2(-8)]²=-7[1/2(-8)]
x²-8x+16=-7+16
(x-4)²=9
x-4=√9
x-4= positive and negative 3
x-4=3    x=3+4     x=7
x-4=-3   x=-3+4    x=1

x²-8x+7=0
(x-7) (x-1)=0
x-7=0        x-1=0
x=7           x=1