can anyone figure out this math problem? Because I sure can't?

Question

x^2 + 16x + a= (X+b)^2

Find a

I have no clue how to do this.

and a must be an integer between 6 and 14.

i mean 60 and 140

Answer 1

x^2 + 16x + a= (X+b)^2

(X+b)^2 = x^2 + 2xb + b^2

So x^2 + 16x + a = x^2 + 2xb + b^2

We can see that
16x = 2xb
So b = 8

We also know that a = b^2
Since b = 8, a = 64

Answer 2

If a must be an integer between 6 and 14, there is
no solution.
Let's complete the square on the left:
x²+16x+64 + a-64 = (x+b)².
(x+8)² + a-64 = (x+b)²
Now like powers of x on both sides must be equal,
so 2b = 16,
b = 8 and a = 64. There is no solution for
a between 6 and 14.