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→Solving quadratic equations
x = 2\mathrm{i}, \, x=-2\mathrm{i}
x = 2\mathrm{i}, \, x=-2\mathrm{i}
</math>
</math>
====Citardauq Formula====
The expression for the quadratic formula above is not in fact unique. If one divides the original quadratic by ''x''<sup>2</sup> to get,
:<math>
a + \frac{b}{x} + \frac{c}{x^2} = 0
</math>
and [[completing the square|completes the square]] in this new expression, a different formula is produced, namely:<ref>{{cite web|url=https://people.csail.mit.edu/bkph/articles/Quadratics.pdf|title=Numerically Stable Method for Solving Quadratic Equations|accessdate=2019-08-03|publisher=people.csail.mit.edu}}</ref>
:<math>
x = \frac{2c}{-b \pm \sqrt{b^2 - 4ac}}
</math>
This formula is useful when ''a'' is small.
===Numerical methods===
Like with many equations, quadratic equations can be solved numerically. However, since any quadratic equation can be solved analytically (non-numerically) using the quadratic formula which provides and exact expression for the solution, this is not often used.
==The discriminant and nature of solutions==
==The discriminant and nature of solutions==