1. State the problem. Solve the quadratic equation $2x^2 - 7x + 1 = 0$. 2. Identify coefficients. Here $a = 2$, $b = -7$, $c = 1$. 3. Write the quadratic formula. The solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 4. Compute the discriminant. Calculate $b^2 - 4ac = (-7)^2 - 4\cdot 2 \cdot 1 = 49 - 8 = 41$. 5. Substitute and simplify. Compute $-b = -(-7) = 7$ and $2a = 4$. Thus $$x = \frac{7 \pm \sqrt{41}}{4}$$ 6. Final answer. The roots are $x = \frac{7 + \sqrt{41}}{4}$ and $x = \frac{7 - \sqrt{41}}{4}$.