Question 333384
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 2x\ -\ 13\ =\ 0]


The factors of -13 are either -1 and 13 or 1 and -13, and neither pair sums to -2.  Therefore this quadratic equation cannot be factored over the rational numbers.


Your alternatives are to complete the square or use the quadratic formula.  Since the quadratic formula requires quite a bit less work, that seems the obvious choice.


The solution to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ ax^2\ +\ bx\ +\ c\ =\ 0]


is


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


so just plug in your coefficients and do the arithmetic.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{-(-2)\ \pm\ \sqrt{(-2)^2\ -\ 4(1)(-13)}}{2(1)}]


You can do your own arithmetic.  Hint for exact answer:  *[tex \Large \sqrt{56}\ =\ \sqrt{4}\,\cdot\,\sqrt{14}\ =\ 2\sqrt{14}] 



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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