Question 321815
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Sorry, can't do what you ask.  You asked to 'factor the following equation'  but then you didn't provide the equation.  You gave a quadratic trinomial.  Equations are called equations because they have an equals sign in them.  *[tex \Large x\ =\ 4] is an equation, but *[tex \Large w\ -\ 3] is NOT an equation and neither is *[tex \Large 64x^2\ -\ 28x\ -\ 64].


Be that as it may, the quadratic trinomial can be factored, but the question is: factored over what set of numbers?


You can take a 4 out of each of the terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 64x^2\ -\ 28x\ -\ 64\ =\ 4\left(16x^2 -\ 7x\ -\ 16\right)]


And since *[tex \LARGE 49\ -\ 4(16)(-16)\ =\ 1073] which is NOT a perfect square, if you are factoring over the rationals, then you are done.


But if you are factoring over the reals, which you can do because *[tex \LARGE 1073\ \geq\ 0], then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 64x^2\ -\ 28x\ -\ 64\ =\ 4\left(x\ -\ \frac{7\ +\ \sqrt{1073}}{32}\right)\left(x\ -\ \frac{7\ -\ \sqrt{1073}}{32}\right)]



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