Solving Radical Equations

Solving a radical equation usually involves three main steps.

Isolate the radical on one side of the equation.
Raise each side of the equation to a power equal to the index of the radical to eliminate the radical.
Solve the resulting equation.
Check the results for extraneous solutions.

Now we can analyze the given radical equation.

- 2 24 x + 13 = - 11

First, let's isolate the radical,

24 x,

on one side of the equation.

- 2 24 x + 13 = - 11

SubEqn

LHS - 13 = RHS - 13

- 2 24 x = - 24

DivEqn

LHS / (- 2) = RHS / (- 2)

24 x = 12

We obtained an isolated radical with index equal to

2 .

Then, we will raise each side of the equation to the power of

2 .

24 x = 12

RaiseEqn

LHS^{2} = RHS^{2}

(24 x)^{2} = 1 2^{2}

Solve for

x

PowSqrt

(a)^{2} = a

24 x = 1 2^{2}

CalcPowCalculate power

24 x = 144

DivEqn

LHS / 24 = RHS / 24

x = 6

Next, we will check for extraneous solutions. We do that by substituting

6

for

x

into the original equation. If the substitution produces a true statement, we know that our answer is correct. If it does not, then it is an extraneous solution.