We want to explain why we should check every solution of a radical equation. To do so, we will write an example radical equation and examine its solutions.
x = sqrt(3-2x)When we solve this equation, we find two different solutions: x= 1 and x= -3. The solving of this can be seen at the bottom of the solution. Now, we will check the solutions by substituting them back into the equation. Let's begin with x= 1.
Notice that x= -3 does not correctly solve our equation, even though it was found as a solution. This is called an extraneous solution. It is very common that raising the sides of a radical equation to an exponent can introduce extraneous solutions. With this in mind, it is good practice to check every solution of a radical equation.
Showing Our Work
Solution to the Example Equation
To solve the example equation, we need to first eliminate the radical. To do so, we will square both sides of the equation and then solve it for x.
