Solving Quadratic Equations using the Quadratic Formula

We'll use the Quadratic Formula to solve the given quadratic equation. $$\begin{array}{c}a{x}^2+bx+c=0\iff x=\frac{\text{-}b\pm \sqrt{b^2-4ac}}{2a}\end{array}$$ We first need to identify the values of $a,$ $b,$ and $c.$ $$\begin{array}{c}2x^2-1x-1=0\iff 2x^2+(\text{-}1)x+(\text{-}1)=0\end{array}$$ We see that $a=2,$ $b=\text{-}1,$ and $c=\text{-}1.$ Let's substitute these values into the Quadratic Formula. The solutions for this equation are $x=\frac{1\pm 3}{4}.$ Let's separate them into the positive and negative cases.

$x=\frac{1\pm 3}{4}$
$x=\frac{1+3}{4}$	$x=\frac{1-3}{4}$
$x=\frac{4}{4}$	$x=\frac{\text{-}2}{4}$
$x=1$	$x=\text{-}\frac{1}{2}$

Using the Quadratic Formula, we found that the solutions of the given equation are $x=1$ and $x=\text{-}\frac{1}{2}.$