I'm preparing for the GRE and was working through an old textbook (chapter on quadratic equations "completing the square," if that helps) and got stumped on $\displaystyle x^2 +{\frac{5x}{a}} + 6x^2 = 10$. Kindly tell me how the author came up with $\displaystyle x= -5 \pm {\frac{\sqrt{305}}{14a}}$?
Thanks.
On
Yes, and the author is wrong. What happened is that he set up the quadratic formula ok. Then at the end he multiplied top and bottom by $a$. He multiplied the $25/a^2$ with $a^2$ which is right but forgot to do that with the $280$ So instead of $280a^2$ he added $25+280=305$
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The author has used the quadratic formula to get the solution.
See the wikipedia page: http://en.wikipedia.org/wiki/Quadratic_equation
Hint: $\displaystyle 7x^2 + \frac{5}{a}x - 10 = 0$. Use quadratic formula to finish.