Example

Solve for $u$: $\quad u = \sqrt{5u+14}$

Solution

The radical is already isolated, so we immediately square both sides:

The resulting equation is quadratic. Let's get a zero on the right-hand side, and then we can use any one of our approaches for solving quadratic equations.

Now we must check these solutions in the original equation.

Let's start with $u=-2$:

Without going any further, we see that $u=-2$ cannot be a solution---an even-indexed radical cannot be negative.

Now let's check $u=7$:

The original equation has the single solution $u=7$.