Explanation Given: The expression: 2 x 2 + 2 = 3 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. 2 x 2 + 2 = 3 x Take the term 3 x at the left-hand side and the constant term to the right-hand side. 2 x 2 + 2 = 3 x 2 x 2 − 3 x = − 2 Divide each term by 2 . 2 x 2 − 3 x = − 2 x 2 − 3 2 x = − 1 Square half of 3 2 = 9 16 . Add 9 16 to both sides of the equation. x 2 − 3 2 x = − 1 x 2 − 3 2 x + 9 16 = − 1 + 9 16 x 2 − 3 2 x + 9 16 = − 7 16 Now, consider the expression

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Chapter 8.1, Problem 43E

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To calculate: The solution for the equation 2x2+2=3x by the method of completing the square.

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Chapter 8.1, Problem 42E

Chapter 8.1, Problem 44E

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The solution for the equation 2 x 2 + 2 = 3 x by the method of completing the square.

Solution Summary: The author calculates the solution for the equation 2x2+2=3x by the method of completing the square.

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