Complete the square for the quadratic a

With the standard form of ax

a = 1, b = 1, c = 6

Solve the quadratic a

We first subtract 6 to isolate our variable on the left side

a

a

a

The amount to add to each side is (½ * middle term coefficient)

Amount to add = | (1 x 1)^{2} |

(2 x 1)^{2} |

Amount to add = | (1)^{2} |

(2)^{2} |

Amount to add = | 1 |

4 |

Amount to add = 1/4

a

(a + 1/2)

Using our LCM Calculator, the Least Common Multiple of our denominators 1 and 4 = 4

We multiply -6 by 4 ÷ 1 = 4 and 1 by 4 ÷ 4 = 1

Simplified Fraction = | -6 x 4 + 1 x 1 |

4 |

Simplified Fraction = | -24 + 1 |

4 |

Simplified Fraction = | -23 |

4 |

We set our left side of the complete the square equation = u

u

u = +√-23/4

u = -√-23/4

a + 1/2 = +NAN

a + 1/2 = -NAN

a + 1/2 - 1/2 = +√/1 - 1/2

Using our LCM Calculator, the Least Common Multiple of our denominators 1 and 2 = 2

We multiply √ by 2 ÷ 1 = 2 and -1 by 2 ÷ 2 = 1

Simplified Fraction = | √ x 2 - 1 x 1 |

2 |

Simplified Fraction = | 0 - 1 |

2 |

Simplified Fraction = | -1 |

2 |

Answer 1 =

a + 1/2 - 1/2 = -√/1 - 1/2

Using our LCM Calculator, the Least Common Multiple of our denominators 1 and 2 = 2

We multiply 0 by 2 ÷ 1 = 2 and -1 by 2 ÷ 2 = 1

Simplified Fraction = | 0 x 2 - 1 x 1 |

2 |

Simplified Fraction = | 0 - 1 |

2 |

Simplified Fraction = | -1 |

2 |

Answer 2 =