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OpenStudy (anonymous):

3r^2+4r+10=0 solve by completing the square r= ??

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jimthompson5910 (jim_thompson5910):

3r^2+4r+10=0 3(r^2+4/3r+10/3)=0 3(r^2+4/3r+4/9-4/9+10/3)=0 3((r+2/3)^2-4/9+10/3)=0 3((r+2/3)^2+26/9)=0 3(r+2/3)^2+3(26/9)=0 3(r+2/3)^2+26/3=0 So after completing the square, you should get \[\large 3(r+\frac{2}{3})^2+\frac{26}{3}=0\]

jimthompson5910 (jim_thompson5910):

\[\large 3(r+\frac{2}{3})^2+\frac{26}{3}=0\] \[\large 3(r+\frac{2}{3})^2=-\frac{26}{3}\] \[\large (r+\frac{2}{3})^2=-\frac{26}{9}\] \[\large r+\frac{2}{3}=\pm\sqrt{-\frac{26}{9}}\] \[\large r+\frac{2}{3}=\pm\frac{i\sqrt{26}}{3}\] \[\large r=-\frac{2}{3}\pm\frac{i\sqrt{26}}{3}\] \[\large r=\frac{-2\pm i\sqrt{26}}{3}\] So the solutions are \[\large r=\frac{-2+ i\sqrt{26}}{3} \textrm{ or }r=\frac{-2- i\sqrt{26}}{3}\]

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