#### The Quadratic Formula

The quadratic formula is used to solve for the roots of a quadratic polynomial (the highest power is 2)

given ax^2+bx+c=0, where a\ne0

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x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} |

Proof using completing the square

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ax^2+bx+c=0 |

multiplying both sides by 4a, we get

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4a^2x^2+4abx+4ac=0 |

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(2a)^2x^2+(2a)(2b)x+b^2=b^2-4ac |

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(2ax+b)^2=b^2-4ac |

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2ax+b=\pm\sqrt{b^2-4ac} |

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2ax=-b\pm\sqrt{b^2-4ac} |

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x=\frac{\pm\sqrt{b^2-4ac}}{2a} |