How do you solve the equation x2−9x=−12 by completing the square?

1 Answer
Shwetank Mauria
May 21, 2017

x=92−√332 or x=92+√332

Explanation:

As we have to solve x2−9x=−12 by completing square method

first have alook at LHS, it appears to be of the form

a2−2ab+b2, where a is x tp find b,

letus write −9x as 2×x×(−92) − an it is apparent that we can use −92 as b and therefore for completing square we must add b2 i.e. (−92)2=814.

Hence we can write x2−9x=−12 as

x2−9x+814=−12+814

i.e. (x−92)2=−48+814=334, which can be written as

(x−92)2=(√332)2

or (x−92)2−(√332)2=0

Now, we can write a2−b2 as (a+b)(a−b) and our equation becomes

(x−92+√332)(x−92−√332)=0

i.e. either x=92−√332 or x=92+√332

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