Question

Solve for x: 2x²-2x-1=0

Answer 1

We can use the quadratic formula to solve this question. The quadratic formula is given below.

`\begin{gathered} ax^2+bx+c=0 \\ \Rightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`

In our case,

`\begin{gathered} a=2,b=-2,c=-1 \\ \Rightarrow x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\cdot2\cdot-1}}{2\cdot2}=\frac{2\pm\sqrt[]{4+8}}{4}=\frac{2\pm\sqrt[]{12}}{4}=\frac{2\pm2\sqrt[]{3}}{4} \\ \Rightarrow x=(1)/(2)\pm\frac{\sqrt[]{3}}{2} \end{gathered}`

Then, the solutions are

`x_1=(1)/(2)+\frac{\sqrt[]{3}}{2},x_2=(1)/(2)-\frac{\sqrt[]{3}}{2}`

The solutions are 1/2+sqrt(3)/2 and 1/2-sqrt(3)/2