Explanation Given Information: The equation is ( x + 3 ) ( x − 1 ) = 5 . 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 the equation, ( x + 3 ) ( x − 1 ) = 5 Simplify as, x 2 + 2 x − 3 = 5 x 2 + 2 x = 8 On comparing x 2 + 2 x + N with the standard form of the quadratic equation a x 2 + b x + n , x 2 + 2 x + N is a complete square, for N = ( 1 2 b ) 2 . Here, b is the coefficient of x . Substitute 2 for b . N = ( 1 2 ( 2 ) ) 2 = ( 1 ) 2 = 1 Thus, the value of N to complete the square for the equation x 2 + 2 x = 8 is 1 . Add 1 on the both sides of the equation, x 2 + 2 x = 8 . Hence, x 2 + 2 x + 1 = 8 + 1 x 2 + 2 x + 1 = 9 Factorize the equation for the calculating the complete square form of the equation. x 2 + x + x + 1 = 9 x ( x + 1 ) + 1 ( x + 1 ) = 9 ( x + 1 ) ( x + 1 ) = 9 ( x + 1 ) 2 = 9 Apply the square root property to simplify the equation

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 55E

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To calculate: The solution of the equation (x+3)(x−1)=5 by completing the square.

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Chapter 11.2, Problem 54E

Chapter 11.2, Problem 56E

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The solution of the equation ( x + 3 ) ( x − 1 ) = 5 by completing the square.

Solution Summary: The author explains how to calculate the solution of the equation (x+3) and the value of N to complete the square.

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To calculate: The solution of the equation (x+3)(x−1)=5 by completing the square.

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