Solve the quadratic equation. \( x^{2}-6 x+25=0 \) Write one exact, simplified solution in each box. You can add or remove boxes. If a solution is not a real number, write it in the form a + bi or \( \mathrm{a}-\mathrm{bi} \), where a and b are real numbers. 믐

To solve the quadratic equation \( x^{2} - 6x + 25 = 0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 1 \), \( b = -6 \), and \( c = 25 \). Plugging in these values: 1. Calculate the discriminant: \[ b^2 - 4ac = (-6)^2 - 4(1)(25) = 36 - 100 = -64 \] Since the discriminant is negative, the solutions will be complex numbers. 2. Now, plug it into the formula: \[ x = \frac{6 \pm \sqrt{-64}}{2 \cdot 1} = \frac{6 \pm 8i}{2} = 3 \pm 4i \] The exact, simplified solutions are: - \( 3 + 4i \) - \( 3 - 4i \)