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.)
4x^2 - x + 1 = 0
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 4x^2 - x + 1 = 0, we identify a = 4, b = -1, and c = 1.
Now, we can substitute these values into the quadratic formula:
x = (-(-1) ± √((-1)^2 - 4(4)(1))) / (2(4))
x = (1 ± √(1 - 16)) / 8
x = (1 ± √(-15)) / 8
Since there is a negative under the square root (√(-15)), we can simplify this solution using the imaginary unit i.
x = (1 ± √(15)i) / 8
Therefore, the solutions to the equation 4x^2 - x + 1 = 0 are:
x = (1 + √(15)i) / 8, (1 - √(15)i) / 8