Solve by completing the square. \( x^{2}-10 x-4=0 \)

To solve the equation \( x^{2} - 10x - 4 = 0 \) by completing the square, first, let's move the constant term to the right side: \( x^{2} - 10x = 4 \). Next, we find the term to complete the square. Take half of the coefficient of \( x \) (which is \(-10\)), square it, and add it to both sides: Half of \(-10\) is \(-5\), and squaring it gives \( 25 \). Adding this to both sides gives: \( x^{2} - 10x + 25 = 4 + 25 \) or \( (x - 5)^{2} = 29 \). Now, take the square root of both sides: \( x - 5 = \pm \sqrt{29} \). Finally, solve for \( x \): \( x = 5 \pm \sqrt{29} \) or \( x = 5 + \sqrt{29} \) and \( x = 5 - \sqrt{29} \). And there you have the solutions!