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When solving the proportion x−26=1x+3, Santos first starts by using the Cross Product Property, multiplying the extremes and the means, to get 6=x2+x−6. Then, he subtracts 6 from both sides of the equation 6=x2+x−6 and finds the equation 0=x2+x−12. Part A: What should Santos do next to solve the equation? Part B: What is/are the solution(s) to the proportion? Select one answer for Part A, and select all answers that apply for Part B.

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sqdancefan

Answer:

  A: factor the equation to (x -3)(x +4) = 0

  B: solutions are x=-4, x=3

Step-by-step explanation:

A: Santos has the equation in standard form. Several options for solution are available: graphing (see attached), completing the square, factoring, using the quadratic formula. I find factoring to get to the solution most directly. The other methods work just as well.

To factor the equation, Santos needs to find two factors of -12 that have a sum of +1. Those would be +4 and -3. Putting these numbers into the binomial factors, Santos would have ...

  (x +4)(x -3) = 0

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B: The values of x that make the factors zero are ...

  x = -4, x = 3

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