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Question

Solve each of the following equations by using the method of completing the square:

x2-2+1x+2=0

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Solution

x2-2+1x+2=0x2-2+1x=-2x2-2×x×2+12+2+122=-2+2+122 Adding 2+122 on both sides
x-2+122=-42+2+1+224=2-22+14=2-122x-2+12=±2-12 Taking square root on both sidesx-2+12=2-12 or x-2+12=-2-12x=2+12+2-12 or x=2+12-2-12
x=222=2 or x=22=1
Hence, 2 and 1 are the roots of the given equation.

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