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Solve the following quadratic equation by completing square method : x^{2} + 10x + 21 = 0.

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#### Solution

x^{2} + 10x + 21 = 0

x^{2} + 10x = -21

To complete the square, find the third term.

`"Third term "=(1/2"coefficient of x")^2`

Coefficient of x=10

`therefore" Third term "=(1/2xx10)^2=(5)^2=25`

Add 25 on both the sides,

x^{2} + 10x + 25=-21+25

(x + 5)^{2} = 4

x + 5 = ± 2 ... Taking square root on both sides

x + 5 = 2 or x + 5=-2

∴ x = -3 or x =-7

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