Use the quadratic formula to solve the equation. \( x^{2}-4 x+10=0 \) The solution set is \( \{\square\} \). (Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

1. Write the equation in standard form: \[ x^2 - 4x + 10 = 0 \] 2. Identify the coefficients: \[ a = 1,\quad b = -4,\quad c = 10 \] 3. Apply the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] 4. Substitute the coefficients: \[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(10)}}{2(1)} = \frac{4 \pm \sqrt{16 - 40}}{2} \] 5. Simplify the expression under the square root: \[ 16 - 40 = -24 \] So, \[ x = \frac{4 \pm \sqrt{-24}}{2} \] 6. Express the square root of the negative number in terms of \( i \): \[ \sqrt{-24} = i\sqrt{24} = i\sqrt{4 \cdot 6} = 2i\sqrt{6} \] Therefore, \[ x = \frac{4 \pm 2i\sqrt{6}}{2} \] 7. Simplify by dividing the numerator by \( 2 \): \[ x = 2 \pm i\sqrt{6} \] 8. The solution set is: \[ \{2 + i\sqrt{6},\; 2 - i\sqrt{6}\} \]