EXAMPLE 4 Solve an equation with an extraneous solution Solve 6 – x = x. 6 – x = x ( 6 – x ) = x 2 2 6 – x = x 2 x – 2 = 0 or x + 3 = 0 0 = x + x – 6 2.

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EXAMPLE 4 Solve an equation with an extraneous solution Solve 6 – x = x. 6 – x = x ( 6 – x ) = x – x = x 2 x – 2 = 0 or x + 3 = 0 0 = x + x – = (x – 2)(x + 3) x = 2 or x = – 3 SOLUTION Write original equation. Square each side. Simplify. Write in standard form. Factor. Zero-product property Solve for x.

EXAMPLE 4 CHECK Check 2 and –3 in the original equation. Solve an equation with an extraneous solution If x = 2: 6 – 2 = 2 ? If x = –3: 6 –(–3) = –3 ? 2 = 23 = –3 ANSWER Because –3 does not check in the original equation, it is an extraneous solution. The only solution of the equation is 2.

EXAMPLE 5 Solve a real-world problem SAILING The hull speed s (in nautical miles per hour) of a sailboat can be estimated using the formula s =1.34 l where l is the length (in feet) of the sailboat’s waterline, as shown. Find the length (to the nearest foot) of the sailboat’s waterline if it has a hull speed of 8 nautical miles per hour.

EXAMPLE 5 The sailboat has a waterline length of about 36 feet. ANSWER SOLUTION Write original equation. Substitute 8 for s. Divide each side by Square each side. Simplify = l 8 = 1.34 l = ( l ) l Solve a real-world problem s = 1.34 l

GUIDED PRACTICE for Examples 4 and 5 5. Solve 3 x + 4 = x. ANSWER 4 6. WHAT IF? In Example 5, suppose the sailboat’s hull speed is 6.5 nautical miles per hour. Find the sailboat’s waterline length to the nearest foot. ANSWER 24 feet