We are asked to solve the equation $x^2 - 6x = 20$ by completing the square.

1. Problem Description

We are asked to solve the equation $x^2 - 6x = 20$ by completing the square.

2. Solution Steps

The equation is $x^2 - 6x = 20$.

To complete the square, we need to add $(b/2)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b = -6$.

So, we add $(-6/2)^2 = (-3)^2 = 9$ to both sides of the equation.

$x^2 - 6x + 9 = 20 + 9$

$x^2 - 6x + 9 = 29$

Now, we can write the left side as a perfect square:

$(x - 3)^2 = 29$

Next, we take the square root of both sides:

$x - 3 = \pm \sqrt{29}$

Finally, we solve for $x$:

$x = 3 \pm \sqrt{29}$

So, the two solutions are $x = 3 + \sqrt{29}$ and $x = 3 - \sqrt{29}$.

3. Final Answer

$3 + \sqrt{29}, 3 - \sqrt{29}$