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. $t=3+i$

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