Explanation Given Information: The provided equation is 6 x + 13 = 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: Step-1: Isolate one of the radical terms on one side of the equation. Step-2: Apply the principle of squaring. Step-3: Perform steps 1 and 2 again if there remains a radical expression in the equation. Step-4: Solve the equation. Step-5: 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, 6 x + 13 = x + 3 Apply the principle of squares and expand using the quadratic expansion, ( 6 x + 13 ) 2 = ( x + 3 ) 2 6 x + 13 = x 2 + 2 ⋅ x ⋅ 3 + 9 6 x + 13 = x 2 + 6 x + 9 Subtract 6 x + 13 from both sides as, 6 x + 13 − ( 6 x + 13 ) = x 2 + 6 x + 9 − ( 6 x + 13 ) 6 x + 13 − 6 x − 13 = x 2 + 6 x + 9 − 6 x − 13 x 2 − 4 = 0 Factorize the polynomial by using the formula A 2 − B 2 = ( A + B </

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 14, Problem 32T

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To calculate: The value of x for the equation 6x+13=x+3.

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Chapter 14, Problem 31T

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The value of x for the equation 6 x + 13 = x + 3 .

Solution Summary: The author explains how to calculate the value of x for the equation sqrt6x+13=x +3.

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Chapter 14 Solutions