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 in standard form

Rewrite \(7x^2 - x = 7\) as \(7x^2 - x - 7 = 0\). Here, \(a = 7\), \(b = -1\), \(c = -7\).

Step2: Apply quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Substitute values: \(x=\frac{-(-1)\pm\sqrt{(-1)^2 - 4(7)(-7)}}{2(7)}\).

Step3: Simplify discriminant

Calculate discriminant: \((-1)^2 - 4(7)(-7)=1 + 196 = 197\).

Step4: Simplify the formula

Substitute discriminant: \(x=\frac{1\pm\sqrt{197}}{14}\).

Answer:

\(\frac{1\pm\sqrt{197}}{14}\) (corresponding to the option \(\frac{1\pm\sqrt{197}}{14}\))