# Other Types of Equations Solving an Equation by Factoring The Power Principle Solve a Radical Equation Solve Equations with Fractional Exponents Solve.

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Other Types of Equations Solving an Equation by Factoring The Power Principle Solve a Radical Equation Solve Equations with Fractional Exponents Solve an Equation in Quadratic Form

Solve An Equation by Factoring Solve: x³ - 16x = 0 x(x² - 16) = 0 x(x + 4)(x – 4) = 0 x = 0 x + 4 = 0 x – 4 = 0 x = 0 x = -4 x = 4 x = -4, 0, 4

Solve A Radical Equation Solve: x = 2 + √2 - x x – 2 = √2 - x x² - 4x + 4 = 2 - x x² - 3x + 2 = 0 (x – 2)(x – 1) = 0 x – 2 = 0 x – 1 = 0 x = 2x = 1 When solving radical equations you must check your solutions.

Solve A Radical Equation Solve: √x + 1 - √2x – 5 = 1 Isolate one of the radicals √x + 1 = 1 + √2x - 5 Square both sides. x + 1 = 1 + 2√2x – 5 + 2x - 5 Isolate the radical -x + 5 = 2√2x - 5 Square both sides x² - 10x + 25 = 4(2x – 5) x² - 10x + 25 = 8x - 20 x² - 18x + 45 = 0 (x – 3)(x – 15) = 0 x – 3 = 0x – 15 = 0 x = 3, 15 Check your solutions

Solve Equations With Fractional Exponents Solve: (x² + 4x + 52) 3/2 = 512 The reciprocal of 3/2 is 2/3, so raise each side to the ⅔ power [(x² + 4x + 52) 3/2 ] ⅔ = 512 ⅔ x² + 4x + 52 = 64 x² + 4x – 12 = 0 (x + 6)(x – 2) = 0 x + 6 = 0 x – 2 = 0 x = -6x = 2 x = {-6, 2}

Solve Equations in Quadratic Form Solve: 4x 4 – 25x² + 36 = 0 Let u² = x 4 and let u = x² 4u² - 25u + 36 = 0 Factor (4u – 9)(u – 4) = 0 4u – 9 = 0u – 4 = 0 u = 9/4 u = 4 Since u = x², substitute x² for u in the solutions x² = 9/4x² = 4 x = + 3/2x = + 2 x = {-2, -3/2, 3/2, 2} There is a table on page 100 that shows different types of equations that are in quadratic form.

Assignment Page 101 # 1 – 63 odd

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