Ex 1: Factor and Solve a Quadratic Equation - a not 1

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This video provides two examples of how to factor and solve a quadratic equation with the leading coefficient not equal to 1 using the trial and error method.
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I'm an engineer and looking back at this. Is there ever any reason that you would do this guess and check and not just use the quadratic formula?

Rag
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the trial and error method is time consuming and stupid

AGarcia