Question 182674
What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0." 
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This is well covered by the onsite solver.
As an example {{{6x^2 - 5x - 21 = 0}}}
*[invoke solve_quadratic_equation 6,-5,-21]
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2 methods are covered, the quadratic equation and factoring.  (The solver gets the factors wrong if the coeff of the x^2 is not 1.)
The 3rd method is completing the square.  Once you know the quadratic equation, use it and forget about completing the square.
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Graphical solutions might be a 4th method.