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Algebra I Notes Section 11.3: Solve Radical Equations Objectives: Students will be able to solve radical equations. An equation that contains a radical expression with a variable in the radicand is a ______________________. radical equation Steps to solve a radical equation: 1. __________________________________________________________________ Isolate one of the radicals on one side of the equation. 2. __________________________________________________________________ Square both sides of the equation, to get the radical to disappear. 3. __________________________________________________________________ Solve the resulting equation for the variable. Check your answers! 4. __________________________________________________________________ Examples: Solve each radical equation. 1. 3 𝑥 − 6 = 0 2. 2 𝑥 + 6 + 9 = 21 3 𝑥=6 2 𝑥 + 6 = 12 𝑥=2 𝑥+6=6 𝑥 2 = 2 𝑥=4 2 𝑥+6 2 = 6 𝑥 + 6 = 36 𝑥 = 30 2 3. 4𝑥 − 12 = 4𝑥 − 12 2 𝑥+3 = 𝑥+3 2 4𝑥 − 12 = 𝑥 + 3 3𝑥 − 12 = 3 3𝑥 = 15 𝑥=5 Squaring both sides of an equation can result in what is called a ___________________________. extraneous solution original equation The answers you get are sometimes not solutions to the ___________________________. So when you square both check sides of an equation you must _____________ your answers. 4. 20 − 𝑥 = 𝑥 20 − 𝑥 2 = 𝑥 5. 6𝑥 − 5 = 𝑥 - 3 2 2 6𝑥 − 5 = 𝑥 − 3 2 20 − 𝑥 = 𝑥 2 6𝑥 − 5 = (𝑥 − 3)(𝑥 − 3) 0 = 𝑥 2 + 𝑥 − 20 6𝑥 − 5 = 𝑥 2 − 3𝑥 − 3𝑥 + 9 0 = 𝑥 2 − 12𝑥 + 14 0 = (𝑥 + 5)(𝑥 − 4) 𝑥+5=0 𝑎𝑛𝑑 𝑥 = −5 𝑥 −4=0 𝑥=4 −𝑏 ± 𝑏 2 − 4𝑎𝑐 𝑥= 2𝑎 12 ± (−12)2 −4(1)(14) 𝑥= 2(1) 4 12 ± 144 − 56 𝑥= 2 12 ± 88 12 ± 2 22 = 6 ± 22 𝑥= = 2 2 𝟔 + 𝟐𝟐