# Completing the Square Examples

### Example 1

Solve by completing the square. -*x*^{2} + 6*x* + 13 = 0 Follow the steps for completing the square. | |

*x*^{2} – 6*x* – 13 = 0
Be careful, because *a* = -1, not *a* = 1 like we need. (*x*^{2} – 6*x* + (3)^{2}) – 13 – 9 = 0 is 3. (*x* – 3)^{2} = 22 and } Square completed. | |

### Example 2

Solve by completing the square. 2*x*^{2} – *x* – 4 = 0 | |

Start by clearing out the *a* term. is Make sure that you have added and subtracted your terms correctly. The fractions being squared can make this difficult. | |

### Example 3

Solve by completing the square. | |

Having a fraction for *a* doesn't really change anything. *x*^{2} + 10*x* + 2 = 0
Just multiply through to clear it out. (*x*^{2} + 10*x* + (5)^{2}) + 2 – (5)^{2} = 0 is 5. (*x* + 5)^{2} = 25 – 2 and | |

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