Question

I would like to know how to solve this problem step by step in depth

Answer 1

Step by step explanation:

Recall that the quadratic formula states that the solutions of the quadratic equation

`ax^2+bx+c=0`

are:

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

Now, to use the quadratic formula we have to take the given equation to ax²+bx+c=0 form:

`\begin{gathered} 11x^2-4x-1=1-1, \\ 11x^2-4x-1=0. \end{gathered}`

Therefore a=11, b=-4, and c=-1.

Substituting the above values in the quadratic formula we get:

`\frac{-(-4)\pm\sqrt[]{(-4)^2-4(11)(-1)}}{2(11)}\text{.}`

Simplifying the above expression we get:

`\begin{gathered} \frac{4\pm\sqrt[]{16+44}}{22}=\frac{4\pm\sqrt[]{60}}{22}=\frac{4\pm\sqrt[]{4\cdot15}}{22} \\ =\frac{4\pm\sqrt[]{4}\sqrt[]{15}}{22}=\frac{4\pm2\sqrt[]{15}}{22} \\ =\frac{2\cdot2\pm2\sqrt[]{15}}{2\cdot11}=\frac{2\pm\sqrt[]{15}}{11}=(2)/(11)\pm\frac{\sqrt[]{15}}{11}\text{.} \end{gathered}`

Answer: First option.