ax^2 + 15x + 4 + 3x + 5 rewrite as
ax^2 +18x + 9
We need to have
( sqrt (a)x + 3)^2 = ax^2 + 18x + 9
a^2 + 2*3sqrt (a) x + 9 =ax^2 + 18x + 9
So
2*3 sqrt (a) = 18
6 sqrt (a) = 18
sqrt (a) = 18 / 6
sqrt (a) = 3 square both sides
a = 9
So we have
( sqrt (9) x + 3)^2 = (3x + 3)^2 = 9x^2 + 18x + 9