Do people know how to complete the square
For Example:
3x2 - 15x + 18 = 0
(Note: 3x2 means 3x squared)
$\displaystyle 3x^2 - 15x + 18 = 0$
$\displaystyle 3(x^2 - 5x + 6) = 0$
$\displaystyle 3\left[x^2 - 5x + \left(-\frac{5}{2}\right)^2 - \left(-\frac{5}{2}\right)^2 + 6\right] = 0$
$\displaystyle 3\left[\left(x - \frac{5}{2}\right)^2 - \frac{25}{4} + \frac{24}{4}\right] = 0$
$\displaystyle 3\left[\left(x - \frac{5}{2}\right)^2 - \frac{1}{4}\right] = 0$
$\displaystyle 3\left(x - \frac{5}{2}\right)^2 - \frac{3}{4} = 0$.
In general, $\displaystyle ax^2+bx+c=a\left(x+\frac{b}{2a}\right)^2 +c-\frac{b^2}{4a}$ , and perhaps you can recognize the term $\displaystyle c-\frac{b^2}{4a}=-\frac{\Delta}{4a}\,,\,\,\Delta=$ the quadratic's discriminant.
So yes, I think some people know how to complete the square.
Tonio