User:Paidgenius/Sandbox

If you found this page without personally knowing, or spying on, Paidgenius (or even finding it when I had forgotten to log out, an unlikely circumstance) well done. Mind you, I hope you leave a message on my talk page explaining how you got here and I will look at all your subpages. Edit it if you want, but though I will only ever delete it manually, I will. OK, there, I've said it. My sandbox is below.

= Quadratics =

$$ ax^2 \pm bx \pm c = 0 $$

To solve quadratic equations, which are of the form shown above, you can use this method:

Example: $$ x^2 - 17x = -66 $$ becomes $$ x^2 - 17x + 66 = 0 $$. Example: $$ a = 1, b = -17, c = 66 $$. Therefore, the formula gives $$ x = \frac {17 \pm \sqrt {289-264}}{2} $$, which comes to $$ 8.5 \pm 2.5 $$. So the two solutions for x are $$ x = 6~or~x = 11 $$.
 * If the quadratic required to solve is not of the form $$ ax^2 \pm bx \pm c = 0 $$, convert it to such a form.
 * Now apply the quadratic formula $$ x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a} $$.

The quadratic formula $$ x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a} $$ can be proved thus:

Any quadratic equation is of the form $$ ax^2 + bx + c = 0 $$, where bx and c may be negative.

= Zero Proof or, 2 = 1 =
 * 1) Let $$ a = b $$
 * 2) Multiply by $$ a $$ - $$ a^2 = ab $$
 * 3) Subtract $$ b^2 $$ -