We need to solve the quadratic equation $2x(8 - 7x) = -11$ for $x$, and round the answers to 2 decimal places.

1. Problem Description

We need to solve the quadratic equation $2x(8 - 7x) = -11$ for $x$, and round the answers to 2 decimal places.

2. Solution Steps

First, expand the expression on the left side of the equation:

$2x(8 - 7x) = 16x - 14x^2$.

Now the equation is $16x - 14x^2 = -11$.

Rearrange the equation to the standard quadratic form $ax^2 + bx + c = 0$:

$-14x^2 + 16x + 11 = 0$.

Multiply by $-1$ to make the leading coefficient positive:

$14x^2 - 16x - 11 = 0$.

Now, we use the quadratic formula to solve for $x$:

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

In this case, $a = 14$, $b = -16$, and $c = -11$.

Plugging these values into the quadratic formula:

$x = \frac{-(-16) \pm \sqrt{(-16)^2 - 4(14)(-11)}}{2(14)}$

$x = \frac{16 \pm \sqrt{256 + 616}}{28}$

$x = \frac{16 \pm \sqrt{872}}{28}$

$x = \frac{16 \pm 2\sqrt{218}}{28}$

$x = \frac{8 \pm \sqrt{218}}{14}$

Now we find the two possible values of $x$:

$x_1 = \frac{8 + \sqrt{218}}{14} \approx \frac{8 + 14.76}{14} \approx \frac{22.76}{14} \approx 1.6257 \approx 1.63$ (to 2 decimal places)

$x_2 = \frac{8 - \sqrt{218}}{14} \approx \frac{8 - 14.76}{14} \approx \frac{-6.76}{14} \approx -0.4829 \approx -0.48$ (to 2 decimal places)

3. Final Answer

$x = 1.63, -0.48$