Explanation Given: The expression: x 2 + 2 = 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 + 2 = x Take the variable x at the left-hand side and the constant term to the right-hand side. x 2 + 2 = x x 2 − x = − 2 Square half of 1 = 1 4 . Add 1 4 to both sides of the equation, x 2 − x = − 2 x 2 − x + 1 4 = − 2 + 1 4 x 2 − x + 1 4 = − 7 4 Now, consider the expression, x 2 − x + 1 4 = ( x ) 2 − 2 ⋅ x ⋅ 1 2 + ( 1 2 ) 2 This expression is of the form a 2 − 2 a b + b 2

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Chapter 8.1, Problem 41E

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To calculate: The solution for the equation x2+2=x by the method of completing the square.

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Chapter 8.1, Problem 40E

Chapter 8.1, Problem 42E

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

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