Question

Which of the following is the result of the equation below after completing the square and function? (x^2 -4x+2=10)

A. ((x-2)^2=14)
B. ((x-2)^2=12)
C. ((x+2)^2=8)
D. ((x+2)^2=14)

Answer 1

To solve the equation (x^2 - 4x + 2) = 10 by completing the square, follow the steps of moving the constant term, adding the square of half the coefficient of x, factoring the trinomial, and taking the square root of both sides. The correct result is ((x - 2)^2 = 12).

Step-by-step explanation:

To solve the equation (x^2 - 4x + 2) = 10 by completing the square, you can follow these steps:

1. Move the constant term 10 to the right side of the equation.
2. Write the quadratic expression as a perfect square trinomial by adding the square of half the coefficient of x. In this case, the coefficient of x is -4, so half of it is -2. To make a perfect square trinomial, add 4 to both sides of the equation.
3. Factor the perfect square trinomial and simplify.
4. Take the square root of both sides of the equation and solve for x.

After following these steps, the equation becomes ((x - 2)^2 = 12). Therefore, the correct answer is B. ((x - 2)^2 = 12).