Question

use the quadratic formula to solve for x.
2x² - 6x - 3 = 0
round your answer to the nearest hundredth.
if there is more than one solution, separate them with commas.
x =

Explanation:

Step1: Identify coefficients

For the quadratic equation $2x^{2}-6x - 3=0$, we have $a = 2$, $b=-6$, $c=-3$.

Step2: Write the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute coefficients

Substitute $a = 2$, $b=-6$, $c=-3$ into the formula:
\[

$$\begin{align*} x&=\frac{-(-6)\pm\sqrt{(-6)^{2}-4\times2\times(-3)}}{2\times2}\\ &=\frac{6\pm\sqrt{36 + 24}}{4}\\ &=\frac{6\pm\sqrt{60}}{4}\\ &=\frac{6\pm2\sqrt{15}}{4}\\ &=\frac{3\pm\sqrt{15}}{2} \end{align*}$$

\]

Step4: Calculate values

First, find $x_1=\frac{3+\sqrt{15}}{2}\approx\frac{3 + 3.873}{2}=\frac{6.873}{2}=3.44$.
Second, find $x_2=\frac{3-\sqrt{15}}{2}\approx\frac{3- 3.873}{2}=\frac{-0.873}{2}=-0.44$.

Answer:

$x = 3.44,-0.44$