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Proofs

Revision as of 20:51, 29 August 2016 by Designerd (talk | contribs) (Created page with "==Quadratic Formula== Let <math>ax^2+bx+c=0</math>. Then <cmath>x^2+\frac{b}{a}x+\frac{c}{a}=0</cmath> Completing the square, we get <cmath>\left(x+\frac{b}{2a}\right)^2 +~ \...")
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Quadratic Formula

Let $ax^2+bx+c=0$. Then \[x^2+\frac{b}{a}x+\frac{c}{a}=0\] Completing the square, we get \[\left(x+\frac{b}{2a}\right)^2 +~ \frac{b^2-4ac}{4a^2}=0 \Rightarrow x~+~\frac{b}{2a}=\pm\sqrt{\frac{b^2-4ac}{4a^2}}=\frac{\pm \sqrt{b^2-4ac}}{2a}\] Simplifying, we see \[\boxed{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}\]

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