Question 772477
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x^2\ =\ 2\ -\ 1x]


Standard form:


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


Factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (3x\ -\ 2)(x\ +\ 1)]


Apply the Zero Product Rule


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x\ -\ 2\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{2}{3}]


Or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 1\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -1]


Check your work:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\left(\frac{2}{3}\right)^2\ =^?\ 2\ -\ \frac{2}{3}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\left(\frac{4}{9}\right)\ =^?\ \frac{6}{3}\ -\ \frac{2}{3}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{3}\ =\ \frac{4}{3}\ \ \ ]Checks.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3(-1)^2\ =^?\ 2\ -\ (-1)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\ =\ 3\ \ \ ] Checks.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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