Explanation Given Information: The provided equation is 3 + 19 − x = 5 + 4 − x . Formula used: The principle of squaring, if a = b , then, a 2 = b 2 The square of the binomial is the square of the first term, plus twice the product of the two terms, plus the square of the last term, ( A + B ) 2 = A 2 + 2 A B + B 2 , where any real number A is the first term and any real number B is the last term. Calculation: Consider the equation, 3 + 19 − x = 5 + 4 − x ………… (1) Subtract 3 from both sides. 3 + 19 − x − 3 = 5 + 4 − x − 3 19 − x = 2 + 4 − x Apply the principle of squaring, and, square both sides, ( 19 − x ) 2 = ( 2 + 4 − x ) 2 19 − x = ( 2 + 4 − x ) 2 Recall that the square of the binomial is the square of the first term, plus twice the product of the two terms, plus the square of the last term, ( A + B ) 2 = A 2 + 2 A B + B 2 , where any real number A is the first term and any real number B is the last term. Substitute 2 for A and 4 − x for B in ( A + B ) 2 = A 2 + 2 A B + B 2 and solve 19 − x = ( 2 + 4 − x ) 2 . 19 − x = ( 2 ) 2 + 2 ( 2 ) ( 4 − x ) + ( 4 − x ) 2 19 − x = 4 + 4 4 − x + 4 − x 19 − x = 8 + 4 4 − x − x Combine the like terms together and isolate the radical

Elementary Algebra: Concepts and Applications (10th Edition)

10th Edition

ISBN: 9780134441375

Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Publisher: PEARSON

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Chapter 8.5, Problem 68ES

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Chapter 8.5, Problem 67ES

Chapter 8.5, Problem 69ES

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Chapter 8 Solutions

Elementary Algebra: Concepts and Applications (10th Edition)

Ch. 8.1 - Find the square roots of 81.Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 3YT Ch. 8.1 - Prob. 4YT Ch. 8.1 - Prob. 5YT Ch. 8.1 - Prob. 6YT Ch. 8.1 - Prob. 7YT Ch. 8.1 - Prob. 8YT Ch. 8.1 - Prob. 1CYU Ch. 8.1 - Prob. 2CYU

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The solution of the equation 3 + 19 − x = 5 + 4 − x .

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Chapter 8 Solutions