Radical equations

When you want to solve an equation with containing a radical expression you have to isolate the radical on one side from all other terms and then square both sides of the equation.


Example

3x=9

x=93=3

(x)2=(3)2

x=9

When you square a radical equation you sometimes get a solution to the squared equation that is not a solution to the original equation. Such an equation is called an extraneous solution. Remember to always check your solutions in the original equation to discard the extraneous solutions.


Example

2x=x

(2x)2=x2

2x=x2

x2+x2=0

x=1±124(2)2

x=1±1+82

x1=1+92=1+32=22=1

x2=192=132=42=2

Here we've got two solutions x = 1 or x = (-2). We check both solutions in the original equation to test whether they are true solutions or extraneous solutions.

21?=1or2(2)?=21=12=2Wrong!

As we could see when we checked our numbers in the original equation x =1 is the only true solution for this equation and that x = -2 is an extraneous solution.


Video lesson

Solve the radical equation

10x=x+2