Solve the quadratic equation. \[ x^{2}-10 x-4=0 \] Write one exact, simplified solution in each box. You can add or remove boxes. If a solutio not a real number, write it in the form a + bi or a - bi, where a and b are real numbers. \( \frac{\square}{\square} \),

To solve the quadratic equation \( x^{2}-10 x-4=0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 1 \), \( b = -10 \), and \( c = -4 \). First, we calculate the discriminant: \[ b^2 - 4ac = (-10)^2 - 4(1)(-4) = 100 + 16 = 116 \] Now, applying the quadratic formula: \[ x = \frac{10 \pm \sqrt{116}}{2} \] Simplifying \( \sqrt{116} \): \[ \sqrt{116} = \sqrt{4 \times 29} = 2\sqrt{29} \] So we have: \[ x = \frac{10 \pm 2\sqrt{29}}{2} = 5 \pm \sqrt{29} \] The two exact, simplified solutions are: \( 5 + \sqrt{29} \), \( 5 - \sqrt{29} \)