Answer
$x=\frac{1+\sqrt{21}}{10}\approx 0.56$ and $x=\frac{1-\sqrt{21}}{10}\approx -0.36$.
Work Step by Step
The given equation is
$\Rightarrow 5x^2-x-1=0$
The equation is not easily factorable. So, solve using the Quadratic formula.
$\Rightarrow 5x^2-x-1=0$
Quadratic formula.
$\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute $5$ for $a,-1$ for $b$ and $-1$ for $c$.
$\Rightarrow x=\frac{-(-1)\pm\sqrt{(-1)^2-4(5)(-1)}}{2(5)}$
Simplify.
$\Rightarrow x=\frac{1\pm\sqrt{1+20}}{10}$
$\Rightarrow x=\frac{1\pm\sqrt{21}}{10}$
Hence, the solutions are $x=\frac{1+\sqrt{21}}{10}\approx 0.56$ and $x=\frac{1-\sqrt{21}}{10}\approx -0.36$.
