(a) Use the quadratic formula to solve \( x^{2}-7 x+3=0 \). Separate multiple answers with a comma, if necessary. Write your answer in exact, simplified form. The solution set is \( \{\square\} \). S

1. Start with the quadratic equation: \[ x^2 - 7x + 3 = 0. \] 2. Identify the coefficients: \( a = 1 \), \( b = -7 \), and \( c = 3 \). 3. Write the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. \] 4. Substitute the values of \( a \), \( b \), and \( c \) into the formula: \[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(1)(3)}}{2(1)}. \] 5. Simplify the expression: \[ x = \frac{7 \pm \sqrt{49 - 12}}{2}, \] \[ x = \frac{7 \pm \sqrt{37}}{2}. \] 6. The solution set is: \[ \left\{\frac{7+\sqrt{37}}{2}, \frac{7-\sqrt{37}}{2}\right\}. \]