Explanation Given Information: The equation 3 − 7 2 p + 2 = 6 ( 2 p + 2 ) 2 Formula used: Step 1:Rewrite the given equation in the form a u 2 + b u + c = 0 where u is a defined variable based on the relationship between the variable expressions in given equation. Step 2: Compute the quadratic equation obtained in Step 1 by applying the zero-factor property and by factoring the trinomial or by using the quadratic formula which is, u = − b ± b 2 − 4 a c 2 a Step 3: Substitute u with the expression it defined in Step 1. Step 4: The resulting equations for the original variable is solved. Step 5: By substituting all the solutions in original equation, check them. Calculation: Consider the equation, 3 − 7 2 p + 2 = 6 ( 2 p + 2 ) 2 …… (1) Simplify the equation, 3 − 7 ( 1 2 p + 2 ) = 6 ( 1 2 p + 2 ) 2 Substitute u for 1 2 p + 2 in equation (1). 3 − 7 u = 6 u 2 Add − 3 + 7 u both sides, 3 − 7 u − 3 + 7 u = 6 u 2 − 3 + 7 u 0 = 6 u 2 + 7 u − 3 Interchange the sides, 6 u 2 + 7 u − 3 = 0 Apply middle term splitting, 6 u 2 + 9 u − 2 u − 3 = 0 Separate out common terms, 3 u ( 2 u + 3 ) − 1 ( 2 u + 3 ) = 0 ( 3 u − 1 ) ( 2 u + 3 ) = 0 Apply zero factor property, 2 u + 3 = 0 2 u = − 3 u = − 3 2 Or, 3 u − 1 = 0 3 u = 1 u = 1 3 Substitute 1 2 p + 2 for u in first solution, 1 2 p + 2 = − 3 2 Multiply 2 p + 2 and − 2 3 both sides, 1 2 p + 2 . ( 2 p + 2 ) ( − 2 3 ) = − 2 3 . ( − 3 2 ) ( 2 p + 2 ) − 2 3 = 2 p + 2 Interchange the sides, 2 p + 2 = − 2 3 Add -2 both sides, 2 p − 2 + 2 = − 2 3 − 2 2 p = − 2 − 6 3 2 p = − 8 3 Divide 2 both sides of solution, 2 p 2 = − 8 3

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 11.4, Problem 68E

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To calculate: The solution to the equation 3−72p+2=6(2p+2)2 and also check it.

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Chapter 11.4, Problem 67E

Chapter 11.4, Problem 69E

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Beginning and Intermediate Algebra (6th Edition)

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The solution to the equation 3 − 7 2 p + 2 = 6 ( 2 p + 2 ) 2 and also check it.

Solution Summary: The author explains how to calculate the solution to the equation 3-72p+2 = ''. Step 3: Substitute u with the expression it defined in Step 1.

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To calculate: The solution to the equation 3−72p+2=6(2p+2)2 and also check it.

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Chapter 11 Solutions