Question

use the quadratic formula to solve for x. 6x² + 8x + 1 = 0 (if there is more than one solution, separate them with commas.) x =

Explanation:

Step1: Identify coefficients

For quadratic $ax^2+bx+c=0$, $a=6$, $b=8$, $c=1$

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

$$b^2-4ac=8^2-4(6)(1)=64-24=40$$

Step4: Substitute into formula

$$x=\frac{-8\pm\sqrt{40}}{2(6)}=\frac{-8\pm2\sqrt{10}}{12}$$

Step5: Simplify the fractions

$$x=\frac{-4\pm\sqrt{10}}{6}$$

Answer:

$\frac{-4+\sqrt{10}}{6}, \frac{-4-\sqrt{10}}{6}$