Explanation Given information: The provided equation is x = 1 + 6 x − 9 . Formula used: Principle of squaring states that if two numbers, a and b are equal, their squares are equal as well. Mathematically, If a = b then a 2 = b 2 Follow the steps to solve the problem: Step1: Isolate one of the radical terms on one side of the equation. Step2: Apply the principle of squaring. Step3: Perform steps 1 and 2 again if there remains a radical expression in the equation. Step4: Solve the equation. Step5: Verify the solutions obtained. The following expansion formula is used: ( a − b ) 2 = a 2 − 2 a b + b 2 In such type of questions, factorize the given polynomial and then apply the principle of zeroes. Principle of zeroes states that if the product of two or more expressions is 0 then either one or two or all of them are 0 . Calculation: Consider the equation, x = 1 + 6 x − 9 Subtract 1 from both the sides, x − 1 = 1 + 6 x − 9 − 1 x − 1 = 6 x − 9 Apply the principle of squares and expand using the quadratic expansion, ( x − 1 ) 2 = ( 6 x − 9 ) 2 x 2 − 2 x + 1 = 36 ( x − 9 ) x 2 − 2 x + 1 = 36 x − 324 Subtract 36 x − 324 from both the sides, x 2 − 2 x + 1 − ( 36 x − 324 ) = 36 x

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 14.5, Problem 28ES

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To calculate: The value of x for the equation x=1+6x−9.

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Chapter 14.5, Problem 27ES

Chapter 14.5, Problem 29ES

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Chapter 14 Solutions

Developmental Mathematics (9th Edition)

Ch. 14.1 - Prob. 1SR Ch. 14.1 - Prob. 2SR Ch. 14.1 - Prob. 1DE Ch. 14.1 - Prob. 2DE Ch. 14.1 - Prob. 3DE Ch. 14.1 - Prob. 4DE Ch. 14.1 - Prob. 5DE Ch. 14.1 - Prob. 6DE Ch. 14.1 - Prob. 7DE Ch. 14.1 - Prob. 8DE

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The value of x for the equation x = 1 + 6 x − 9 .

Solution Summary: The author calculates the value of x for the equation, which is 13,25, and applies the principle of squaring.

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To calculate: The value of x for the equation x=1+6x−9.

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Chapter 14 Solutions