Example: The product of some negative number and 5 less than twice that number is 273. Find the number.

Solution: Translate the statement into an equation and then solve the equation.

“The product of some negative number…”

Let x be some negative number and multiply that number by the expression that comes next in the statement.

“…and 5 less than twice that number…”

5 less than means take 5 away from what follows. Twice that number refers to 2 times the negative number that was described before. (2x-5)

“…is 273”

This translates to equals 273.

Solve the equation.

Use the distributed property to rewrite the equation (recognize that the equation is a quadratic equation) | |

Choose the method for solving the quadratic equation (factoring, square root method, completing the square or quadratic formula) I will demonstrate factoring so I need to move all terms to the same side to have zero on one side. | |

Factor | |

Use the zero product property and set each factor equal to zero and solve. |

Since the statement says that the number is negative, the number is .