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EXAMPLE 2 Solve a Radical Equation 3 4 5, you need to isolate the radical To solve the equation 2x expression first. 2x 345 Write the original equation. 2x 31 Subtract 4 from each side of the equation. (2x 3 )2 12 Square each side of the equation. 2x 3 1 Simplify the equation. 2x 4 Add 3 to each side of the equation. x2 Divide each side of the equation by 2. ANSWER 䊳 The solution is 2. Check the solution in the original equation. Solve a Radical Equation Solve the equation. 1. x 3 2. m 4 0 3. x 64 4. n 11 5. x 4 5 11 6. 3n 131 Squaring both sides of an equation can introduce a solution to the squared equation that does not satisfy the original equation. Such a solution is called an extraneous solution. When you solve by squaring both sides of an equation, check each solution in the original equation. EXTRANEOUS SOLUTIONS Student Help MORE EXAMPLES 3 Check for Extraneous Solutions Solve x2 x and check for extraneous solutions. NE ER T More examples are available at www.mcdougallittell.com INT EXAMPLE Solution x2 x Write the original equation. (x2)2 x 2 Square each side of the equation. x 2 x2 Simplify the equation. x2 x 2 0 Write the equation in standard form. (x 2)(x 1) 0 Factor the equation. Use the zero-product property to solve for x. CHECK ✓ Substitute 2 and 1 in the original equation. 2 2 ⱨ 2 22✓ ANSWER 䊳 x 2 or x 1 1 2 ⱨ 1 1 1 The only solution is 2, because x 1 does not satisfy the original equation. 12.3 Solving Radical Equations 705