**So far, we have studied the four methods to solve a quadratic equation. How do we select the best method to solve among these four methods?**

**The following table will guide us to choose the best method to solve.**

Method | When to choose |

Use if we need only the appropriate solutions. However, we can use it always. | |

Use if we could easily determine the factors or the constant term is zero. | |

Use if the equation is of the form x^{2} + bx + c = 0 and b is even. However, we can use it always. | |

We can use this method to any type of quadratic equation. In some cases, the other methods will be easy to solve. |

**Example:**

**The product of two consecutive positive odd integers is 99. Find those two numbers.**

**Solution:**

**Step 1:**

**Given that the product of two consecutive positive odd integers is 99.**

**We are asked to find the two consecutive positive odd integers.**

**Let the first integer be**

*x*.**Then the consecutive positive odd integer is**

*x*+ 2.**Given that the product of**

*x*and*x*+ 2 = 99**=>**

*x*(*x*+ 2) = 99**=>**

*x*^{2}+ 2*x*- 99 = 0**So, we arrived at a quadratic equation**

*x*^{2}+ 2*x*- 99 = 0.**Step 2:**

**We can solve the quadratic equation by using factoring.**

*x*^{2}+ 11*x*- 9*x*- 99 = 0**=>**

*x*(*x*+ 11) - 9(*x*+ 11) = 0**=> (**

*x*+ 11)(*x*- 9) = 0**=>**

*x*+ 11 = 0 or*x*- 9 = 0**=>**

*x*= -11 or*x*= 9**Step 3:**

**Since we are looking for a positive number, neglect -11.**

**So,**

*x*= 9.**If**

*x*= 9, then*x*+ 2 = 9 + 2 = 11.**Step 4:**

**Hence, the two consecutive positive odd numbers are 9 and 11.**

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