Solve for the roots in simplest form by completing the square: -6x^2-96x-330=0 Answer Attempt 1out of 2 (C) Additional Solution ()No Solution z=1

To solve the quadratic equation $-6x^{2}-96x-330=0$ by completing the square, we first divide the entire equation by -6 to simplify it:<br /><br />$x^{2}+16x+55=0$<br /><br />Next, we move the constant term to the other side of the equation:<br /><br />$x^{2}+16x=-55$<br /><br />Now, we complete the square by adding $\left(\frac{16}{2}\right)^{2}=64$ to both sides:<br /><br />$x^{2}+16x+64=-55+64$<br /><br />$(x+8)^{2}=9$<br /><br />Taking the square root of both sides, we get:<br /><br />$x+8=\pm3$<br /><br />Finally, solving for $x$, we find the roots:<br /><br />$x_{1}=-8+3=-5$<br />$x_{2}=-8-3=-11$<br /><br />Therefore, the roots of the equation $-6x^{2}-96x-330=0$ are $x_{1}=-5$ and $x_{2}=-11$.