Question

In the following exercises, solve by using the Quadratic Formula.
$2x^2-x+1=0$

Short answer

The solutions of the given equation are $x=\frac{1}{4}\pm \frac{\sqrt{7}}{4}i$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$2x^2-x+1=0$

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a{x}^2+bx+c=0$is:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

In the given equation, $a=2,b=-1,c=1$. Substitute these values in Quadratic Formula.

$x=\frac{-(-1)\pm \sqrt{(-1{)}^2-4(2\left)\right(1)}}{2\left(2\right)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl}x& =& \frac{1\pm \sqrt{1-8}}{4}\\ x& =& \frac{1\pm \sqrt{-7}}{4}\\ x& =& \frac{1}{4}\pm \frac{\sqrt{-7}}{4}\\ x& =& \frac{1}{4}\pm \frac{\sqrt{7}}{4}i[\because \sqrt{-1}=i]\end{array}$

Step 4. Conclusion.

The solutions of the given equation are $x=\frac{1}{4}\pm \frac{\sqrt{7}}{4}i$.