Explanation Given Information: The equation is x 2 + ( x + 1 ) 2 = 25 . Formula used: The square of sum of two terms a and b is simplified as, ( a + b ) 2 = a 2 + b 2 + 2 a b According to the principle of zero products, if a b = 0 , then, a = 0 or b = 0 Calculation: Consider the equation, x 2 + ( x + 1 ) 2 = 25 …… (1) Simplify the equation using ( a + b ) 2 = a 2 + b 2 + 2 a b , x 2 + x 2 + 1 2 + 2 ⋅ 1 ⋅ x = 25 2 x 2 + 2 x + 1 = 25 Subtract 25 from both sides, to make right hand side value zero, 2 x 2 + 2 x + 1 − 25 = 25 − 25 2 x 2 + 2 x − 24 = 0 2 ⋅ x 2 + 2 ⋅ x − 2 ⋅ 12 = 0 Take 2 common from the left-hand side, 2 ( x 2 + x − 12 ) = 0 x 2 + x − 12 = 0 Factorize the equation, x 2 + 4 x − 3 x − 12 = 0 x ( x + 4 ) − 3 ( x + 4 ) = 0 (

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 2PTMO

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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, x 2 + ( x + 1 ) 2 = 25 .

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