Explanation Given Information: The provided equation is x + 3 = 8 x − 9 . 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 factorize the trinomial by using ac-method: Step 1: Factor out a common factor from the trinomial of the form a x 2 + b x + c . Step 2: Find the product of the coefficient of the x 2 , that is a and the constant c . Step 3: Factor the product a c such that the sum of the factors is equal to b , that is there are two integers p and q such that p × q = a × c and p + q = b . Step 4: Write the middle term by splitting it as a sum of the factors obtained in step ( 3 ) . Step 5: Factorize the polynomial by grouping. Step 6: Verify by multiplying. 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, x + 3 = 8 x − 9 Apply principle of squaring, x + 3 = 64 x − 9 Multiply both the sides by x − 9 , ( x + 3 ) ( x − 9 ) = 64 x 2 − 9 x + 3 x − 27 = 64 x 2 − 6 x − 27 = 64 Subtract 64 from both the sides of the equation, x 2 − 6 x − 27 − 64 = 64 − 64 x 2 − 6 x − 91 = 0 Multiply the coefficient of x 2 , that is 1 and the constant − 91 , 1 ( − 91 ) = − 91 Factor − 91 such that the sum of the factors is equal to the middle term − 6

16th Edition

ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 14.5, Problem 63ES

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To calculate: The value of x for the equation x+3=8x−9.

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Chapter 14.5, Problem 62ES

Chapter 14.5, Problem 64ES

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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 x + 3 = 8 x − 9 .

Solution Summary: The author explains the principle of squaring, which states that if two numbers are equal, then their squares are also equal.

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Chapter 14 Solutions