Question

using the quadratic formula to solve $7x^2 - x = 7$, what are the values of $x$?\
\\(\frac{1\pm\sqrt{195}i}{14}\\)\
\\(\frac{1\pm\sqrt{197}}{14}\\)\
\\(\frac{1\pm\sqrt{195}}{14}\\)\
\\(\frac{1\pm\sqrt{197}i}{14}\\)

Explanation:

Step1: Rewrite to standard quadratic form

$7x^2 - x - 7 = 0$

Step2: Identify a, b, c values

$a=7,\ b=-1,\ c=-7$

Step3: Compute discriminant $\Delta$

$\Delta = b^2 - 4ac = (-1)^2 - 4(7)(-7) = 1 + 196 = 197$

Step4: Apply quadratic formula

$x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{1 \pm \sqrt{197}}{14}$

Answer:

$\boldsymbol{\frac{1\pm\sqrt{197}}{14}}$ (matches the second option: $\frac{1\pm\sqrt{197}}{14}$)