Question 199793
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x^2 = -4x - 20]


The first thing you need to do is to put your equation into standard form, namely: *[tex \Large ax^2 + bx + c = 0]


So just add *[tex \Large 4x + 20] to both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x^2 + 4x + 20 = 0]


The quadratic formula is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = \frac{-b \pm sqrt{b^2 - 4ac}}{2a} ]


So just plug in the values of the coefficients:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = \frac{-(4)\pm sqrt{(4)^2-4(3)(20)}}{2(3)}]


And do the arithmetic.


The discriminant (the part under the radical) is negative in this case, so you will end up with a conjugate pair of complex roots.  Just factor -1 out of the radicand and take out an *[tex \Large i] which is defined as *[tex \Large i^2 = -1]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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