Solve by completing the square: 4. x^2-6x-8=0

To solve the quadratic equation $x^{2}-6x-8=0$ by completing the square, we first move the constant term to the other side of the equation:<br /><br />$x^{2}-6x=8$<br /><br />Next, we take half of the coefficient of $x$, which is $-6$, and square it. Half of $-6$ is $-3$, and $(-3)^{2}=9$. We add $9$ to both sides of the equation:<br /><br />$x^{2}-6x+9=8+9$<br /><br />Simplifying, we get:<br /><br />$(x-3)^{2}=17$<br /><br />Taking the square root of both sides, we have:<br /><br />$x-3=\pm\sqrt{17}$<br /><br />Finally, solving for $x$, we get:<br /><br />$x=3\pm\sqrt{17}$<br /><br />So the solutions to the equation $x^{2}-6x-8=0$ are $x=3+\sqrt{17}$ and $x=3-\sqrt{17}$.