Use the quadratic formula to find the exact solutions of the following equation. \( x^{2}-3 x=10 \) \( x=\square \) (Simplify your answers. Type exact answers, using radicals as needed. Use a comma to separate answers as needed. Express complex numbers in terms of \( i \). Type each solution only once.)

To solve the equation \( x^{2} - 3x - 10 = 0 \) using the quadratic formula, we first identify the coefficients: \( a = 1 \), \( b = -3 \), and \( c = -10 \). The quadratic formula is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Now we plug in the coefficients into the formula: \[ x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-10)}}{2(1)} \] Calculating inside the square root: \[ (-3)^2 = 9 \] \[ -4(1)(-10) = 40 \] \[ 9 + 40 = 49 \] Now, taking the square root of 49: \[ \sqrt{49} = 7 \] Now substitute back into the formula: \[ x = \frac{3 \pm 7}{2} \] This gives us two solutions: \[ x = \frac{3 + 7}{2} = \frac{10}{2} = 5 \] \[ x = \frac{3 - 7}{2} = \frac{-4}{2} = -2 \] So the exact solutions are: \( x = 5, -2 \)