Question

Please help if you can I’m not understanding this I appreciate it thank you so much

Answer 1

`B)\text{ }x=\frac{1\pm2\sqrt[]{3}}{3}`

Step-by-step explanation

To solve this, first, we have to subtract 11 from both sides of the equation,

`\begin{gathered} 9x^2-6x-11=11-11 \\ \\ 9x^2-6x-11=0 \end{gathered}`

Now, the equation is in the form,

`ax^2+bx+c=0`

And we can apply the quadratic formula,

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

In this case, a = 9, b = -6, and c = -11,

`x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot9\cdot(-11)}}{2\cdot9}=\frac{6\pm\sqrt[]{36+396}}{18}=\frac{6\pm\sqrt[]{432}}{18}=\frac{6\pm12\sqrt[]{3}}{18}`

We can simplify this by factoring out 6 in both the numerator and denominator,

`x=\frac{6((6)/(6)\pm(12)/(6)\sqrt[]{3})}{6((18)/(6))}=\frac{1\pm2\sqrt[]{3}}{3}`

Hence, the answer is option B.