Explanation:
Dividing each side of the equation by 3 will not change the solutions to the equation, so this step is fine. However, adding the square of to each side of the equation will not result in a completed square and will not yield the correct solutions to the equation.
To solve the equation 3x^2 - 5x = 4 by completing the square, you can follow these steps:
Write the equation in the form ax^2 + bx + c = 0, where a, b, and c are constants. In this case, a = 3, b = -5, and c = 4.
Add the square of half of the coefficient of the x term (b/2) to both sides of the equation. In this case, that would be (b/2)^2 = (-5/2)^2 = (5/4)^2 = (25/16).
Factor the left side of the equation. In this case, the left side becomes (3x - (5/2))^2 = 25/16.
Take the square root of both sides of the equation. In this case, this gives us 3x - (5/2) = sqrt(25/16) or 3x - (5/2) = -sqrt(25/16).
Solve for x in each equation. In this case, the solutions are x = (5/6) + sqrt(25/16)/3 or x = (5/6) - sqrt(25/16)/3.
These are the solutions to the equation 3x^2 - 5x = 4