Question

use the quadratic formula to solve for x.
\\(7x^2 + 3x - 2 = 0\\)
if there is more than one solution, separate them with commas.
\\(x = \square\\)

Explanation:

Step1: Identify coefficients

For $7x^2 + 3x - 2 = 0$, $a=7$, $b=3$, $c=-2$

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

$b^2 - 4ac = 3^2 - 4(7)(-2) = 9 + 56 = 65$

Step4: Substitute into formula

$$x = \frac{-3 \pm \sqrt{65}}{2(7)} = \frac{-3 \pm \sqrt{65}}{14}$$

Answer:

$\frac{-3 + \sqrt{65}}{14}, \frac{-3 - \sqrt{65}}{14}$