Explanation Given Information: The provided equation is 2 x − 5 − 1 = x − 3 . Formula used: Principle of squaring states that if two numbers, a and b are equal, then their squares are also equal, that is if a = b then a 2 = b 2 also true. To solve the square root radical equation, follow the below steps: Step1: Isolate one of the radical terms from the given equation on one side of the equation. Step2: Apply the principle of squaring. Step3: Perform the step 1 and 2 again if there remains a radical expression in the equation. Step4: Simplify the equation. Step5: Verify all the obtained solutions. To apply the principal of squaring, use the given formula: ( a − b ) 2 = a 2 − 2 a b + b 2 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 , that is ( x − a ) ⋅ ( x − b ) = 0 Then, either ( x − a ) = 0 or, ( x − b ) = 0 Calculation: Consider the equation, 2 x − 5 − 1 = x − 3 Since, the radical term x − 3 is already present at one side of the equation Apply the principle of squaring and use the formula ( a − b ) 2 = a 2 − 2 a b + b 2 , ( 2 x − 5 − 1 ) 2 = x − 3 2 x − 5 − 2 2 x − 5 + 1 = x − 3 2 x − 4 − 2 2 x − 5 = x − 3 Subtract 2 x from both sides of the equation, 2 x − 4 − 2 2 x − 5 − 2 x = x − 3 − 2 x − 4 − 2 2 x − 5 = − x − 3 Add 4 to both the sides of the equation to isolate the radical, − 4 − 2 2 x − 5 + 4 = − x − 3 + 4 − 2 2 x − 5 = − x + 1 2 2 x − 5 = 1 − x Now, the radical term 2 2 x − 5 is at one side of the equation

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ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 14.5, Problem 44ES

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To calculate: The value of x for the equation 2x−5−1=x−3.

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Chapter 14.5, Problem 43ES

Chapter 14.5, Problem 45ES

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The value of x for the equation 2 x − 5 − 1 = x − 3 .

Solution Summary: The author explains how to solve the square root radical equation by applying the principle of squaring.

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To calculate: The value of x for the equation 2x−5−1=x−3.

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Chapter 14 Solutions