Final answer:
To solve the quadratic equation 2m² - 1m + 5 = 2 using the quadratic formula, it's rearranged to 2m² - 1m + 3 = 0. The quadratic formula yields two complex solutions, m = (1/4) ± (√23/4)i.
Step-by-step explanation:
To solve the equation using the quadratic formula, you must first rearrange the equation to set it equal to zero. The equation 2m² - 1m + 5 = 2 can be rearranged to 2m² - 1m + 3 = 0. Once in this form, we can apply the quadratic formula, m = (-b ± √(b² - 4ac)) / (2a), where a = 2, b = -1, and c = 3.
Now plug in the values and calculate the determinant (b² - 4ac), which gives us (-1)² - 4(2)(3) = 1 - 24 = -23. Since the determinant is negative, the equation has two complex solutions. The solutions are:
m = (1 ± √(-23)) / 4. Thus, the two solutions for m are complex numbers and can be written as:
m = (1/4) ± (√23/4)i, where 'i' is the imaginary unit.