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Obtain the characteristic equation
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$r^{2}+3r+6=0$
Learn how to solve equations problems step by step online. Solve the differential equation x^''+3x^'6x=0. Obtain the characteristic equation. Find the solutions to the quadratic equation r^{2}+3r+6=0. Take only the positive solution (the one where the coefficient of i is greater than 0). Express the complex root (r=\frac{-3+\sqrt{15}i}{2}) in the form r=a+bi where a and b are constants.