Explanation Given Information: The provided equation is x 2 − 8 x + 12 = 0 . Formula used: To solve an equation a x 2 + b x + c = 0 by completing the square, (1) If a ≠ 1 , multiply the equation a x 2 + b x + c = 0 by 1 a so that the coefficient of x 2 is 1. (2) Add or subtract c a so that the equation is in the form x 2 + b a x = − c a . (3) Take half of the coefficient of x and square it. Add the result on both sides of the equation. (4) Use the principle of square roots and complete the solution. According to the square root principle, if a 2 = b , then, a = b or a = − b The solutions can be represented by a = ± b . Calculation: Consider the provided equation, x 2 − 8 x + 12 = 0 Add − 12 to both sides of the equation, x 2 − 8 x + 12 − 12 = 0 − 12 x 2 − 8 x = − 12 Apply completing the square method where b = − 8 , ( 1 2 b ) 2 = ( 1 2 ( − 8 ) ) 2 = ( − 4 ) 2 = 16 Add 16 both sides of the equation, x 2 − 8 x = − 12 x 2 − 8 x = − 12 x 2 − 8 x + 16 = − 12 + 16 x 2 − 8 x + 16 = 4 Factorize the equation to calculate the complete square form of the equation, x 2 − 4 x − 4 x + 16 =

Intermediate Algebra For College Students (9th Edition)

9th Edition

ISBN: 9780321927354

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 8, Problem 5RE

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To calculate: The solution of the equation x2−8x+12=0 by completing the square.

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Chapter 8, Problem 4RE

Chapter 8, Problem 6RE

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Chapter 8 Solutions

Intermediate Algebra For College Students (9th Edition)

Ch. 8.1 - Fill in the blanks with the appropriate word,...Ch. 8.1 - Fill in the blanks with the appropriate word,...Ch. 8.1 - Prob. 3ES Ch. 8.1 - Prob. 4ES Ch. 8.1 - Fill in the blanks with the appropriate word,...Ch. 8.1 - Prob. 6ES Ch. 8.1 - Prob. 7ES Ch. 8.1 - Prob. 8ES Ch. 8.1 - Prob. 9ES Ch. 8.1 - Prob. 10ES

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The solution of the equation x 2 − 8 x + 12 = 0 by completing the square.

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Chapter 8 Solutions