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Question

Solve each of the following equation by using the method of completing the square:
x28x2=0 ?

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Solution

We will use the difference of squares identity ,which can be written
a2b2=(ab)(a+b) with
a=(x+4) and
b=14 as follows:
0=x2+8x+2=(x+4)216+2
=(x+4)2(14)2
=((x+4)14)((x+4)+14)
=(x+414)((x+4+14)
Hence:x=4±14
x=144 OR
x=144
x=0.258 OR
x=7.742

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