Question

For quadratic equation x2-6x=16 what should be the third term to make LHS a complete square

Answer 1

$x^{2}-6x = 16\\\\LHS = x^{2} -6x$

Before finding the third term we will revise how does it looks like when expanding a complete square as below,

$(a+b)^{2}= a^{2}+2ab + b^{2}$

So in our question,

$(x-m)^{2} = x^{2} -6x + Third term$

When we expand this,

$x^{2} +2.(x).(-m) +(-m)^{2} \\x^{2} -2xm +m^{2} \\\\2xm = -6x\\2m = -6\\m=-3$

So the third term is,

$m^{2} = (-3)^{2}$

$m^{2} = 9$

Answer is +9