Explanation Given Information: The provided equation is 12 5 x + 6 = 2 x + 5 . 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. 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, 12 5 x + 6 = 2 x + 5 Apply the principle of squaring, 144 5 x + 6 = 2 x + 5 Multiply both the sides with 5 x + 6 , 144 = ( 2 x + 5 ) ( 5 x + 6 ) ( 5 x + 6 ) ( 2 x + 5 ) = 144 10 x 2 + 25 x + 12 x + 30 = 144 10 x 2 + 37 + 30 = 144 Subtract 144 from both the sides of the equation, 10 x 2 + 37 + 30 − 144 = 144 − 144 10 x 2 + 37 − 114 = 0 Multiply the coefficient of x 2 , that is 10 and the constant − 114 , 10 ( − 144 ) = − 1440 Factor − 1440 such that the sum of the factors is equal to the middle term 37

16th Edition

ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 14.5, Problem 64ES

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To calculate: The value of x for the equation 125x+6=2x+5.

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Chapter 14.5, Problem 63ES

Chapter 14.6, Problem 1SR

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The value of x for the equation 12 5 x + 6 = 2 x + 5 .

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

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Chapter 14 Solutions