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

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To solve the quadratic equation $$ x^{2} - 10x - 4 = 0 $$ by completing the square, follow these steps:

1. **Move the constant term to the other side:**
   $$
   x^{2} - 10x = 4
   $$

2. **Complete the square:**
   - Take half of the coefficient of $$ x $$, which is $$-10$$:
     $$
     \frac{-10}{2} = -5
     $$
   - Square this value:
     $$
     (-5)^2 = 25
     $$
   - Add this square to both sides of the equation:
     $$
     x^{2} - 10x + 25 = 4 + 25
     $$
     $$
     (x - 5)^2 = 29
     $$

3. **Solve for $$ x $$ by taking the square root of both sides:**
   $$
   x - 5 = \pm \sqrt{29}
   $$
   $$
   x = 5 \pm \sqrt{29}
   $$

**Final Answer:**
The solutions are $$ x = 5 + \sqrt{29} $$ and $$ x = 5 - \sqrt{29} $$.
The solutions are $$ x = 5 + \sqrt{29} $$ and $$ x = 5 - \sqrt{29} $$.

Solve by completing the square.

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