Question 175846
{{{x^2+16x+a=(x+b)^2}}} Start with the given equation.



{{{x^2+16x+a=x^2+2xb+b^2}}} FOIL the right side.


Take note that the terms 16x and 2xb both have "x" terms (without an exponent). So this means that {{{16x=2xb}}}. Divide both sides by 2x to get {{{8=b}}} or {{{b=8}}}


Notice how the term "a" does not have an "x" and {{{b^2}}} doesn't have an "x" either. So this means that {{{a=b^2}}}.



Plug in {{{b=8}}} to get {{{a=8^2=64}}}. So {{{a=64}}}



So this tells us that {{{x^2+16x+64=(x+8)^2}}}