Explanation Given Information: The provided equation is x − 1 = x + 5 . 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. 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 . Square of differences, ( a − b ) 2 = a 2 − 2 a b + b 2 Calculation: Consider the equation, x − 1 = x + 5 Apply the principle of squares and expand using the quadratic expansion, ( x − 1 ) 2 = ( x + 5 ) 2 x 2 − 2 x + 1 = x + 5 Subtract x and 5 from both the sides, x 2 − 3 x − 4 = 0 Factorize by splitting the middle term, x 2 − 4 x + x − 4 =

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Chapter 14.5, Problem 4DE

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To calculate: The value of x in for the equation x−1=x+5.

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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 in for the equation x − 1 = x + 5 .

Solution Summary: The author explains how to calculate the value of x in a given equation by applying the principle of squaring.

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