Question

In the following exercises, solve by using the Quadratic Formula.

$8x^2-6x+2=0$

Short answer

The solutions of the given equation are $x=\frac{3}{8}\pm \frac{\sqrt{7}}{8}i$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$8x^2-6x+2=0$

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, $a=8,b=-6,c=2$. Substitute these values in Quadratic Formula.

$x=\frac{-(-6)\pm \sqrt{(-6{)}^2-4(8\left)\right(2)}}{2\left(8\right)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl}x& =& \frac{6\pm \sqrt{36-64}}{16}\\ x& =& \frac{6\pm \sqrt{-28}}{16}\\ x& =& \frac{6}{16}\pm \frac{\sqrt{-28}}{16}\\ x& =& \frac{3}{8}\pm \frac{2\sqrt{-7}}{16}\\ x& =& \frac{3}{8}\pm \frac{\sqrt{7}}{8}i[\because \sqrt{-1}=i]\end{array}$

Step 4. Conclusion.

The solutions of the given equation are $x=\frac{3}{8}\pm \frac{\sqrt{7}}{8}i$.