Final answer:
To complete the square of the quadratic equation 2x^2 + 2 = 3x, subtract 3x from both sides and divide by 2 to simplify the equation. Then, take half of the coefficient of x, square it, and add it to both sides. Rearrange the equation to have a perfect square form (x - h)^2 = k.
Step-by-step explanation:
To complete the square of the quadratic equation 2x^2 + 2 = 3x, we need to rearrange the equation in the form (x - h)^2 = k. Start by subtracting 3x from both sides to get 2x^2 - 3x + 2 = 0. Then, divide the equation by 2 to have a coefficient of 1 in front of x^2.
The equation now becomes x^2 - (3/2)x + 1 = 0. To complete the square, take half of the coefficient of x and square it, which is (3/4)^2 = 9/16. Add this value to both sides of the equation:
x^2 - (3/2)x + 9/16 + 1 = 0 + 9/16
Simplify the left side by converting the expression into a perfect square: (x - 3/4)^2 = 7/16. Therefore, the complete square form of the quadratic equation 2x^2 + 2 = 3x is (x - 3/4)^2 = 7/16.