Explanation Given Information: The equation is x 2 − 4 x = − 3 . Formula used: The standard form of the quadratic equation is, a x 2 + b x + n = 0 Here, a , b , and n are the constants or number. Also, if the above quadratic equation is a perfect square. Then, n = [ 1 2 ( b ) ] 2 Here, b is the coefficient of x . Calculation: Consider the provided equation, x 2 − 4 x = − 3 On comparing x 2 − 4 x + N with the standard form of the quadratic equation a x 2 + b x + n , the equation x 2 − 4 x + N is a complete square, for N = ( 1 2 b ) 2 . Substitute − 4 for b . N = ( 1 2 ( − 4 ) ) 2 = ( − 2 ) 2 = 4 Thus, the value of N to complete the square for the equation x 2 − 4 x = − 3 is 4 . Hence, Add 4 on the both sides of the equation, x 2 − 4 x = − 3 . x 2 − 4 x + 4 = − 3 + 4 x 2 − 4 x + 4 = 1 On completing the square, by factorizing, x 2 − 2 x − 2 x + 4 = 1 x ( x − 2 ) − 2 ( x − 2 ) =<

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 11.2, Problem 23E

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To calculate: The solution of the equation x2−4x=−3 by completing the square.

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Chapter 11.2, Problem 22E

Chapter 11.2, Problem 24E

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Chapter 11 Solutions

Beginning and Intermediate Algebra (6th Edition)

Ch. 11.1 - Concept Check Answer each question. 1. Which of...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 6E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 8E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 10E

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The solution of the equation x 2 − 4 x = − 3 by completing the square.

Solution Summary: The author calculates the solution of the equation x2-4x=-3 by completing the square.

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To calculate: The solution of the equation x2−4x=−3 by completing the square.

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Chapter 11 Solutions