Explanation Given: The expression: x 2 + 5 = 4 x . Formula used: Square root property. If x 2 = a , then x = ± a for all real numbers a . The identity of square of difference of two values. ( a − b ) 2 = a 2 − 2 a b + b 2 Here, a and b are any two-real values. The square root of the negative numbers is given by the method of including the imaginary number i , where i 2 = − 1 . Calculation: Consider the expression. x 2 + 5 = 4 x Take the variable 4 x at the left-hand side and the constant term to the right-hand side. x 2 + 5 = 4 x x 2 − 4 x = − 5 Square half of 4 = 4 . Add 4 to both sides of the equation. x 2 − 4 x = − 5 x 2 − 4 x + 4 = − 5 + 4 x 2 − 4 x + 4 = − 1 Now, consider the expression, x 2 − 4 x + 4 = ( x ) 2 − 2 ⋅ x ⋅ 2 + ( 2 ) 2 This expression is of the form a 2 − 2 a b + b 2

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ISBN: 9780134188515

Author: Crawford

Publisher: YUZU

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Chapter 8.1, Problem 42E

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To calculate: The solution for the equation x2+5=4x by the method of completing the square.

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Chapter 8.1, Problem 41E

Chapter 8.1, Problem 43E

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The solution for the equation x 2 + 5 = 4 x by the method of completing the square.

Solution Summary: The author calculates the solution for the equation x2+5=4x by the method of completing the square.

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To calculate: The solution for the equation x2+5=4x by the method of completing the square.

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