Explanation Definition used: General quadratic equation : “Given that a , b , and c are constant ( a ≠ 0 ) , the equation a x 2 + b x 2 + c = 0 is called the general quadratic equation in x ”. Calculation: Consider the equation ( x 2 + 5 x ) 2 − 5 ( x 2 + 5 x ) = 6 . In order to find the value of x , first rewrite the equation in quadratic form. Substitute y = x 2 + 5 x in ( x 2 + 5 x ) 2 − 5 ( x 2 + 5 x ) = 6 and simplify the equation as follows. y 2 − 5 y − 6 = 0 y 2 − 6 y + y − 6 = 0 y ( y − 6 ) + 1 ( y − 6 ) = 0 y − 6 = 0 or y + 1 = 0 On further simplification, y = 6 or y = − 1 x 2 + 5 x = 6 or x 2 + 5 x = − 1 [ ∵ y = x 2 + 5 x ] x 2 + 5 x − 6 = 0 or x 2 + 5 x + 1 = 0 ( x + 6 ) ( x − 1 ) = 0 or x 2 + 5 x + 1 = 0 On further simplification, x + 6 = 0 or x − 1 = 0 or x = − 5 ± 25 − 4 ( 1 ) ( 1 ) 2 x = − 6 or x = 1 or x = − 5 + 21 2 or − 5 − 21 2 Thus, the solution of the equation is x = − 6 , 1 , − 5 + 21 2 and − 5 − 21 2 . Check the solution by substituting x = − 6 in ( x 2 + 5 x ) 2 − 5 ( x 2 + 5 x ) = 6 . ( ( − 6 ) 2 + 5 ( − 6 ) ) 2 − 5 ( ( − 6 ) 2 + 5 ( − 6 ) ) = ? 6 ( 36 − 30 ) 2 − 5 ( 36 − 30 ) = ? 6 ( 6 ) 2 − 5 ( 6 ) = ? 6 36 − 30 = ? 6 6 = 6 [ True ] Check the solution by substituting x = 1 in ( x 2 + 5 x ) 2 − 5 ( x 2 + 5 x ) = 6

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 14, Problem 38RE

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To solve: The equation (x2+5x)2−5(x2+5x)=6.

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Chapter 14, Problem 37RE

Chapter 14, Problem 39RE

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Chapter 14 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

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 2 + 5 x ) 2 − 5 ( x 2 + 5 x ) = 6 .

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To solve: The equation (x2+5x)2−5(x2+5x)=6.

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Chapter 14 Solutions