Question

use the quadratic formula to solve for x. 2x^2 - 2x - 9 = 0 (if there is more than one solution, separate them with commas.) x =

Explanation:

Step1: Identify coefficients

For the quadratic equation $2x^{2}-2x - 9=0$, we have $a = 2$, $b=-2$, $c=-9$.

Step2: Recall quadratic formula

The quadratic formula for a quadratic equation $ax^{2}+bx + c = 0$ is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute coefficients

Substitute $a = 2$, $b=-2$, $c=-9$ into the formula:
\[

$$\begin{align*} x&=\frac{-(-2)\pm\sqrt{(-2)^{2}-4\times2\times(-9)}}{2\times2}\\ &=\frac{2\pm\sqrt{4 + 72}}{4}\\ &=\frac{2\pm\sqrt{76}}{4}\\ &=\frac{2\pm2\sqrt{19}}{4}\\ &=\frac{1\pm\sqrt{19}}{2} \end{align*}$$

\]

Answer:

$x=\frac{1+\sqrt{19}}{2},\frac{1 - \sqrt{19}}{2}$