The problem is to solve the quadratic equation $x^2 - 11x + 6 = 0$.

1. Problem Description

The problem is to solve the quadratic equation $x^2 - 11x + 6 = 0$.

2. Solution Steps

We can use the quadratic formula to solve for $x$.

The quadratic formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In our equation, $x^2 - 11x + 6 = 0$, we have $a = 1$, $b = -11$, and $c = 6$.

Plugging these values into the quadratic formula, we get:

$x = \frac{-(-11) \pm \sqrt{(-11)^2 - 4(1)(6)}}{2(1)}$

$x = \frac{11 \pm \sqrt{121 - 24}}{2}$

$x = \frac{11 \pm \sqrt{97}}{2}$

So, the two solutions for $x$ are:

$x = \frac{11 + \sqrt{97}}{2}$ and $x = \frac{11 - \sqrt{97}}{2}$.

3. Final Answer

The solutions are $x = \frac{11 + \sqrt{97}}{2}$ and $x = \frac{11 - \sqrt{97}}{2}$.