How the quadratic formula works:
For any quadratic equation ax² + bx + c = 0, the solution is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex].
In the case of our equation 7x² - x = 7, first we need to subtract 7 from each side so that we have 0 on the right.
7x² - x - 7 = 0
Identify the values of a, b, and c.
a = 7, b = -1, and c = -7.
Plug these into our quadratic formula and solve.
[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(7)(-7)}}{2(7)}=\boxed{\frac{1\pm\sqrt{197}}{14}[/tex]
There are two values for x: (1+√197)/14 and (1-√197)/14.
The approximate values for these are 1.073976 and -0.931119.
