When you have a quadratic in the form ax² + bx + c = 0, you can solve for x using the quadratic formula, which is as follows:
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
In this case, a = 2, b = -2, and c = -1. Let's plug these in.
\(x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(-1)}{2(2)}\)
Simplify...
\(x=\frac{2\pmsqrt{4+8}}4\)
\(x=\frac{2\pmsqrt{12}}4\)
\(\sqrt{12}=\sqrt{2\times2\times3}=2\sqrt{3}\)
\(x=\frac{2\pm2\sqrt{3}}4\)
\(x=\frac{1\pm\sqrt{3}}2\)
\(\boxed{x=\frac{1+\sqrt{3}}2\ or\ \frac{1-\sqrt{3}}2}\)
