Explanation Given Information: A provided radical equation is x + 3 = 7 . Consider a radical equation is, x + 3 = 7 ………… (1) The principle of squaring, if a = b , then, a 2 = b 2 Apply the principle of squaring, and, square both sides, ( x + 3 ) 2 = 7 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 x for A and 3 for B in ( A + B ) 2 = A 2 + 2 A B + B 2 and solve ( x + 3 ) 2 = 7 2 . ( x ) 2 + 2 ( x ) ( 3 ) + 3 2 = 49 x + 6 x + 9 = 49 Subtract 9 from both sides, x + 6 x + 9 − 9 = 49 − 9 x + 6 x = 40 Subtract x from both sides, x + 6 x − x = 40 − x 6 x = 40 − x Apply the principle of squaring, and, square both sides, ( 6 x ) 2 = ( 40 − x ) 2 Substitute 40 for A and x for B in ( A − B ) 2 = A 2 − 2 A B + B 2 and solve ( 6 x ) 2 = ( 40 − x ) 2 . ( 6 x ) 2 = ( 40 − x ) 2 36 x = ( 40 ) 2 − 2 ( 40 ) x + x 2 36 x = 1600 − 80 x + x 2 Subtract 36 x from both sides, 36 x − 36 x = 1600 − 80 x + x 2 − 36 x 0 = 1600 − 116 x + x 2 Factor 1600 − 116 x + x 2

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 60ES

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Whether the radical equation x+3=7 can be solved without isolating the radical before squaring.

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Chapter 8.5, Problem 59ES

Chapter 8.5, Problem 61ES

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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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Whether the radical equation x + 3 = 7 can be solved without isolating the radical before squaring.

Solution Summary: The author explains that the radical equation sqrtx+3=7 can be solved without isolating it before squaring.

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Whether the radical equation x+3=7 can be solved without isolating the radical before squaring.

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Chapter 8 Solutions