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Are the two solutions to x (2x+1) = 1 found by setting x = 1 and 2x + 1 = 1? Explain your reasoning. What are the solutions to this equation? Show how you arrived at your answer. Create an equation for your classmates to solve that requires factoring.

  • math - ,

    nope. Just because two numbers multiply together to make 1, you still know nothing about the numbers.

    If nothing else, try your idea.
    If x=1, 2x+1=3, and 1*3≠1

    However, if two numbers multiply to be zero, then one or the other must be zero. So, let's set things equal to xero, rather than 1.

    x(2x+1) - 1 = 0
    2x^2 + x - 1 = 0
    you can factor that to get
    (2x-1)(x+1) = 0

    Now you have two possibilities:
    2x-1 = 0
    x+1 = 0

    So, that gives you two solutions for x:
    x = 1/2
    x = -1

    To verify that they satisfy the original equation, plug them in:

    (1/2)(1+1) = 1
    (-1)(-1) = 1

    So we are good.

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