### Solving quadratics of the form x^{2} + bx + c = 0 by factorising first

This means find the values of x where the quadratic x^{2} + bx + c = 0 This can be done as follows:

| **i.** | | Factorise x^{2} + bx + c = 0 into the form (x + n)(x + q) This has already been shown in Factorising Quadratics − 1 |

| **ii.** | | So (x + n)(x + q) = 0 |

| **iii.** | | The values in either of the above brackets must equal to 0, as brackets means multiply and anything multipled by 0 is equal to 0. So: |

| x + n = 0 | | => | | x = −n | | or |

| x + q = 0 | | => | | x = −q | | |

#### Example 1. Solve x^{2} + 7x + 6 = 0

**iii.** | | x + 1 = 0 | | => | | x = −1 | | Or |

| | x + 6 = 0 | | => | | x = −6 | | |

#### Example 2. Solve x^{2} − 11x + 30 = 0

**iii.** | | x − 5 = 0 | | => | | x = 5 | | Or |

| | x − 6 = 0 | | => | | x = 6 | | |

#### Example 3. Solve x^{2} + 2x − 8 = 0

**iii.** | | x + 4 = 0 | | => | | x = −4 | | Or |

| | x − 2 = 0 | | => | | x = 2 | | |

#### Example 4. Solve x^{2} − 5x − 24 = 0

**iii.** | | x + 3 = 0 | | => | | x = −3 | | Or |

| | x − 8 = 0 | | => | | x = 8 |

#### Remember:

Find the values of x where x^{2} + bx + c = 0 is the same as solve x^{2} + bx + c = 0

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