# Completing the sqare

Input interpretation |
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complete the square | 28 + 10 x + x^2 |

Result |

(x + 5)^2 + 3 |

Geometric figure |

parabola |

Polynomial discriminant |

Delta = -12 |

Derivative |

d/dx((x + 5)^2 + 3) = 2 (x + 5) |

Indefinite integral |

integral (3 + (5 + x)^2) dx = x^3/3 + 5 x^2 + 28 x + constant |

Global minimum |

min{(x + 5)^2 + 3} = 3 at x = -5 |