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4.5 Solve Quadratic Equations by Finding Square Roots

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EXAMPLE 1 Use properties of square roots Simplify the expression. 5= 4a = = 3 14b = 9 14 = c = 4 = 2929 d = 7 = 4 7

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GUIDED PRACTICE for Example ANSWER

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GUIDED PRACTICE for Example ANSWER

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GUIDED PRACTICE for Example ANSWER

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GUIDED PRACTICE for Example ANSWER

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EXAMPLE 2 Rationalize denominators of fractions. Simplify (a) 5 2 and SOLUTION (a) = = 5 2 = (b)

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EXAMPLE 2 Rationalize denominators of fractions. SOLUTION (b) = – 2 2 = 21 – – – 2 22 = 21 – 32 47

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EXAMPLE 3 Solve a quadratic equation Solve 3x = 41. 3x = 41 Write original equation. 3x 2 = 36 Subtract 5 from each side. x 2 = 12 Divide each side by 3. x = + 12 Take square roots of each side. x = Product property Simplify.

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EXAMPLE 3 Solve a quadratic equation ANSWER The solutions are and – Check the solutions by substituting them into the original equation. 3x = 41 3( ) = ? 41 = 41 3(12) + 5 = 41 ? 3x = 41 3( ) = 41 – 2 3 ? 41 = 41 3(12) + 5 = 41 ?

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EXAMPLE 4 Standardized Test Practice SOLUTION 1515 (z + 3) 2 = 7 Write original equation. (z + 3) 2 = 35 Multiply each side by 5. z + 3 = + 35 Take square roots of each side. z = – Subtract 3 from each side. The solutions are –3 + and –3 – 35

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EXAMPLE 4 Standardized Test Practice ANSWER The correct answer is C.

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GUIDED PRACTICE for Examples 2, 3, and 4 GUIDED PRACTICE Simplify the expression ANSWER – 21 – – 6 7 – 5 8 – ANSWER

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– for Examples 2, 3, and 4 GUIDED PRACTICE 15. – – 3 ANSWER

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for Examples 2, 3, and 4 GUIDED PRACTICE 17. Solve the equation. 5x 2 = z 2 – 7 = (x – 2) 2 = ANSWER

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