Solve the equation #t^2+10=6t# by completing square method?

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Answer 1 · 2016-10-27T06:00:34

#t=3-i# or #t=3+i#

#t^2+10=6t# can be written as

#t^2-6t+10=0#

or #t^2-6t+9+1=0#

Now we use the identity #(x+1)^2=x^2+2x+1# and imaginary number #i# defined by #i^2=-1#

or #t^2-2xx3t+3^2-(-1)=0#

or #(t-3)^2-i^2=0#

Now using identity #a^2-b^2=(a+b)(a-b)#, this becomes

#(t-3+i)(t-3-i)=0#

Hence, either #t-3+i=0# i.e. #t=3-i#

or #t-3-i=0# i.e. #t=3+i#