## To solve the quadratic equation 2x^2 - x + 2 = 0, you can use the factoring method.

Step 1: Write down the equation: 2x^2 - x + 2 = 0.

Step 2: Try to factor the equation by splitting the middle term. Look for two numbers that multiply to give the product of the coefficient of x^2 and the constant term, and add up to the coefficient of x. In this case, the coefficient of x^2 is 2, the constant term is 2, and the coefficient of x is -1. We need to find two numbers that multiply to give 2 * 2 = 4 and add up to -1. The numbers are -2 and -2.

Step 3: Rewrite the middle term using the two numbers found in Step 2: 2x^2 - 2x - 2x + 2 = 0.

Step 4: Group the terms and factor by grouping: (2x^2 - 2x) + (-2x + 2) = 0.

Step 5: Factor out the common factors in each group: 2x(x - 1) - 2(x - 1) = 0.

Step 6: Notice that (x - 1) is a common factor in both terms. Factor it out: (x - 1)(2x - 2) = 0.

Step 7: Simplify the factored expression: (x - 1)(2(x - 1)) = 0.

Step 8: Simplify further: (x - 1)(2x - 2) = 0.

Step 9: Apply the zero-product property, which states that if a product of two factors equals zero, then at least one of the factors must be zero. Set each factor equal to zero and solve for x:

x - 1 = 0 -> x = 1.

2x - 2 = 0 -> 2x = 2 -> x = 1.

Step 10: The solutions to the equation 2x^2 - x + 2 = 0 are x = 1.

Therefore, the correct factored form of the equation is (2x - 2)(x + 1) = 0.