Use the quadratic formula to solve the equation. (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)
2x^2 - x + 6 = 0
To solve the quadratic equation 2x^2 - x + 6 = 0 using the quadratic formula, we will first identify the coefficients a, b, and c.
In this case, a = 2, b = -1, and c = 6.
The quadratic formula states that the solutions of a quadratic equation ax^2 + bx + c = 0 can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Now let's substitute the values into the formula:
x = (-(-1) ± √((-1)^2 - 4(2)(6))) / (2(2))
Simplifying,
x = (1 ± √(1 - 48)) / 4
x = (1 ± √(-47)) / 4
Since we have a square root of a negative number, we can simplify it further using the imaginary unit, i:
x = (1 ± √47i) / 4
So the solutions to the equation 2x^2 - x + 6 = 0 are:
x = (1 + √47i) / 4, (1 - √47i) / 4