As we have to solve x^2-9x=-12x2−9x=−12 by completing square method
first have alook at LHS, it appears to be of the form
a^2-2ab+color(red)(b^2)a2−2ab+b2, where aa is xx tp find bb,
letus write -9x−9x as 2xx x xx (-9/2)2×x×(−92) -− an it is apparent that we can use -9/2−92 as bb and therefore for completing square we must add color(red)(b^2)b2 i.e. (-9/2)^2=81/4(−92)2=814.
Hence we can write x^2-9x=-12x2−9x=−12 as
x^2-9x+color(red)(81/4=-12+color(red)(81/4)x2−9x+814=−12+814
i.e. (x-9/2)^2=(-48+81)/4=33/4(x−92)2=−48+814=334, which can be written as
(x-9/2)^2=(sqrt33/2)^2(x−92)2=(√332)2
or (x-9/2)^2-(sqrt33/2)^2=0(x−92)2−(√332)2=0
Now, we can write a^2-b^2a2−b2 as (a+b)(a-b)(a+b)(a−b) and our equation becomes
(x-9/2+sqrt33/2)(x-9/2-sqrt33/2)=0(x−92+√332)(x−92−√332)=0
i.e. either x=9/2-sqrt33/2x=92−√332 or x=9/2+sqrt33/2x=92+√332
