Question

use the quadratic formula to solve for x.
7x^2 - 6x + 1 = 0
(if there is more than one solution, separate them wit
x =

Explanation:

Step1: Identify coefficients

For the quadratic equation $7x^{2}-6x + 1=0$, we have $a = 7$, $b=-6$, $c = 1$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac=(-6)^{2}-4\times7\times1=36 - 28=8$.

Step3: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substituting the values, we get $x=\frac{6\pm\sqrt{8}}{2\times7}=\frac{6\pm2\sqrt{2}}{14}=\frac{3\pm\sqrt{2}}{7}$.

Answer:

$x=\frac{3 + \sqrt{2}}{7},\frac{3-\sqrt{2}}{7}$