Solve the equation $8 - ext{\sqrt{11 - 2x}} = -x$, giving your answer in the form $a + b\sqrt{c}$, where $a$, $b$ and $c$ are integers.

1. Isolate the surd term on one side of the equation.

$8 + x = \sqrt{11 - 2x}$

2. Square both sides to eliminate the square root and form a quadratic equation.

$(8 + x)^2 = 11 - 2x$
$64 + 16x + x^2 = 11 - 2x$
$x^2 + 18x + 53 = 0$

3. Solve the quadratic equation using the quadratic formula.

$x = \frac{-18 \pm \sqrt{18^2 - 4(1)(53)}}{2}$
$x = \frac{-18 \pm \sqrt{324 - 212}}{2}$
$x = \frac{-18 \pm \sqrt{112}}{2}$

4. Simplify the surd and check for extraneous solutions.

$\sqrt{112} = \sqrt{16 \times 7} = 4\sqrt{7}$
$x = \frac{-18 \pm 4\sqrt{7}}{2} = -9 \pm 2\sqrt{7}$

Check the solutions in the original equation (or note that $8 + x \ge 0$):
If $x = -9 - 2\sqrt{7}$, $8 + x = -1 - 2\sqrt{7} < 0$, which is invalid since a principal square root cannot be negative.
If $x = -9 + 2\sqrt{7}$, $8 + x = -1 + 2\sqrt{7} > 0$, which is valid.

Therefore, $x = -9 + 2\sqrt{7}$.