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1. Identify a = 4, b = -11, c = -3.
2. Plug the values into the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a).
3. Simplify: x = (11 ± √((-11)^2 - 4(4)(-3)))/(2(4)).
4. Continue simplifying: x = (11 ± √169)/8.
5. Simplify further: x = (11 ± 13)/8.
6. Separate into two equations: x = (11 + 13)/8 and x = (11 - 13)/8.
7. Simplify: x = 24/8 and x = -2/8.
8. Continue simplifying: x = 3 and x = -1/4.