Find all solutions of the equation \( x^{2}-8 x+36=0 \) by using the quadratic formula. \( x= \) Hint: Express the soutions in the form \( a+b i, a-b i \).

To solve the equation \( x^{2} - 8x + 36 = 0 \) using the quadratic formula, we start with the formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 1 \), \( b = -8 \), and \( c = 36 \). Plugging these values into the formula gives: \[ x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4 \cdot 1 \cdot 36}}{2 \cdot 1} \] \[ x = \frac{8 \pm \sqrt{64 - 144}}{2} \] \[ x = \frac{8 \pm \sqrt{-80}}{2} \] Next, simplifying \( \sqrt{-80} \): \[ \sqrt{-80} = \sqrt{80} \cdot i = \sqrt{16 \cdot 5} \cdot i = 4\sqrt{5} \cdot i \] Now we can plug this back into the equation for \( x \): \[ x = \frac{8 \pm 4\sqrt{5} i}{2} \] \[ x = 4 \pm 2\sqrt{5} i \] Thus, the solutions are: \[ x = 4 + 2\sqrt{5} i, \quad x = 4 - 2\sqrt{5} i \]