Answer
5
Work Step by Step
We know:
$$(x+2)(x+7) = 84 \\ x^2 + 7x+2x +14 = 84 \\ x^2+9x-70=0$$
Since the coefficient of the squared term is one, we know that the expression must factor to:
$$ (x\pm a)(x\pm b)$$
Here, we see that a and b must multiply to get $-70$ and add to get $9$. Thus, we find that the solution is:
$$(x+14)(x-5)$$
Thus, setting each factor equal to zero, we find that the solutions are:
$$ x=-14,5$$
x must be positive, so:
$$x=5$$
