Explanation Definition used: General quadratic equation : “Given that a , b , and c are constant ( a ≠ 0 ) , the equation a x 2 + b x + c = 0 is called the general quadratic equation in x ”. Calculation: Consider the equation x − 3 x − 2 = 6 . In order to find the value of x , first rewrite the equation in quadratic form. Substitute y = x − 2 in x − 3 x − 2 = 6 and simplify the equation as follows. x − 2 − 4 − 3 x − 2 = 0 y 2 − 3 y − 4 = 0 y 2 − 4 y + y − 4 = 0 y ( y − 4 ) + 1 ( y − 4 ) = 0 ( y − 4 ) ( y + 1 ) = 0 On further simplification, y − 4 = 0 or y + 1 = 0 x − 2 = 4 or x − 2 = − 1 [ ∵ x − 2 ] x − 2 = 16 or x − 2 = 1 x = 18 or x = 3 Thus, the solutions of the equation are x = 3 and x = 18

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Author: Washington

Publisher: PEARSON

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Chapter 14.3, Problem 21E

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To solve: The equation x−3x−2=6 algebraically.

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Chapter 14.3, Problem 20E

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Chapter 14 Solutions

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Ch. 14.1 - In Example 7, determine how many times the rocket...Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E

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The equation x − 3 x − 2 = 6 algebraically.

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