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Solving an Equation with Two Radical Terms

Example

Solve for x:

Solution

Step 1 Isolate a radical term.

Subtract from both sides.

Step 2 Apply the Principle of Powers.

 

= 2

 

Square both sides.
Step 3 Solve the resulting equation.

Write the right side as a product.

FOIL the right side.
Isolate the remaining radical term. 2x - 6
Divide both sides by 2. x - 3
Square both sides. (x - 3)2
Write the left side as a product.

Simplify.

Write in standard form.

Factor.

Use the Zero Product Property.

Solve for x.

Step 4 Check the solution.

(x - 3)(x - 3)

x2 - 6x + 9

x2 - 10x - 21

(x - 3)(x - 7)

x - 3 = 0 or x - 7

x = 3 or x

= 4(x - 3)

= 4x - 12

= 0

= 0

= 0

= 7

Since x = 7 does not check, the only solution is x = 3.

Note:

We divide both sides by 2 rather than 4 in order to avoid introducing fractions into the equation.

One way to simplify is:

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