Explanation Given information: The provided equation is 27 − 3 x = x − 3 . 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, 27 − 3 x = x − 3 Apply the principle of squares and expand using the quadratic expansion, ( 27 − 3 x ) 2 = ( x − 3 ) 2 27 − 3 x = x 2 − 6 x + 9 Subtract 27 − 3 x from both the sides, 27 − 3 x − ( 27 − 3 x ) = x 2 − 6 x + 9 − ( 27 − 3 x ) 0 = x 2 − 3 x − 18 x 2 − 3 x − 18 = 0 Factorize the polynomial by splitting the middle term, x 2 + 3 x − 6

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Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 14.5, Problem 26ES

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To calculate: The value of x for the equation 27−3x=x−3.

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Chapter 14 Solutions

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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 27 − 3 x = x − 3 .

Solution Summary: The author explains how to calculate the value of x for the equation sqrt27-3x=x-3.

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