sat-dog

The correct answer is $5$. Multiplying both sides of the given equation by $x+6$ results in $55=x\left(x+6\right)$. Applying the distributive property of multiplication to the right-hand side of this equation results in $55=x^2+6x$. Subtracting $55$ from both sides of this equation results in $0=x^2+6x-55$. The right-hand side of this equation can be rewritten by factoring. The two values that multiply to $-55$ and add to $6$ are $11$ and $-5$. It follows that the equation $0=x^2+6x-55$ can be rewritten as $0=\left(x+11\right)\left(x-5\right)$. Setting each factor equal to $0$ yields two equations: $x+11=0$ and $x-5=0$. Subtracting $11$ from both sides of the equation $x+11=0$ results in $x=-11$. Adding $5$ to both sides of the equation $x-5=0$ results in $x=5$. Therefore, the positive solution to the given equation is $5$.