Question 183214
If {{{ax^2 + 12x + c}}} is a square, it can be expressed as
(1) {{{(sqrt(a)*x + sqrt(c))^2}}}
performing the square, I get
{{{ax^2 + 2*sqrt(a)*sqrt(c)*x + c}}}
{{{ax^2 + sqrt(4ac)*x + c}}}
Comparing this with 
{{{ax^2 + 12x + c}}}
{{{12 = sqrt(4ac)}}}
square both sides
{{{144 = 4ac}}}
{{{ac = 36}}}
{{{c = 36/a}}}
{{{c}}} should be a perfect square
If {{{c > a}}},
{{{a = 4}}} and
{{{9 = 36/4}}} is the only possibility
{{{ax^2 + 12x + c = 4x^2 + 12x + 9}}} answer