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2x^2-3x-9=0

you must get what is equal to zero

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Ali M. | Friendly and High Quality TutoringFriendly and High Quality Tutoring
4.8 4.8 (4 lesson ratings) (4)
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2x^2-3x-9=0 can be factored as 1/2*(2x-6)*(2x+3)=0 so we can simplify and get (x-3)*(2x+3)=0

and so x= 3 or x= -3/2

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.9 4.9 (51 lesson ratings) (51)
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The goal here is to solve for the unknown variable, x. That is, you want to find the value(s) of x the equation will equal to zero.

To solve for x, you have to factor the polynomial function to generate two binomials whose produce equals zero. Then, by the zero product property, we can set each binomial equal to zero and solve for x.

         2x2 - 3x - 9 = 0

    (2x + 3)(x - 3) = 0

Set each binomial equal to zero:

      2x + 3 = 0                  and                 x - 3 = 0

            - 3     - 3                                         + 3     + 3

  ______________                               _______________

             2x = -3                                              x = 3

      (2x)/2 = (-3)/2

             x = -3/2

Thus,   2x2 - 3x - 9 = 0   when   x = -3/2   and when   x = 3