Answer
$x=6$
Work Step by Step
First square both sides: $x^2=5x+6$
Then move the $5x+6$ to the left-hand side to create a quadratic: $x^2-5x-6=0$
Use the quadratic formula to solve for possible values of $x$:
The quadratic formula states that for a quadratic $ax^2+bx+c$, the two possible roots take the form $\frac{-b+\sqrt{b^2-4ac}}{2a}$ or $\frac{-b-\sqrt{b^2-4ac}}{2a}$.
We see that the two possible roots of our equation are $\frac{5+\sqrt{49}}{2}=6$ and $\frac{5-\sqrt{49}}{2} = -1$.
Looking back at our original equation, we see that $x$ is the square root of a number. Because the square root of a number cannot be negative, we see that $x=6$ is the only solution to this equation.
