Question 117946
Here's one approach you could try.

{{{x^2+16x+a = (x+b)^2}}} Expand the right side.
{{{x^2+16x+a = x^2+2bx+b^2}}} Subtract {{{x^2}}} from both sides.

{{{16x+a = 2bx+b^2}}} Now equate the x-terms.
{{{16x = 2bx}}} Divide by 2x.
{{{8 = b}}}
Now equate the constant terms.
{{{a = b^2}}} but b = 8, so...
{{{a = 8^2}}} and...
{{{a = 64}}}