Solve the quadratic equation by Completing the Square

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\[\begin{aligned} &3 x^2+4 x-15=0 \\\\ &x^2+\frac{4}{3} x-5=0 \\\\ &x^2+2\left(\frac{2}{3}\right) x+\left(\frac{2}{3}\right)^2-\left(\frac{2}{3}\right)^2-5=0 \\\\ &\left(x+\frac{2}{3}\right)^2=5+\frac{4}{9} \\\\ &\left(x+\frac{2}{3}\right)^2=\frac{45}{9}+\frac{4}{9} \\\\ &\left(x+\frac{2}{3}\right)^2=\frac{49}{9} \\\\ &x+\frac{2}{3}=\pm \frac{7}{3} \\\\ &x=\pm \frac{7}{3}-\frac{2}{3} \\\\ &x=\frac{7}{3}-\frac{2}{3} \text { or } x=\frac{-7}{3}-\frac{2}{3} \\\\ &x=\frac{5}{3} \text { or } x=-3 \end{aligned}\]

\[\text {Thus, the solution set}=\left\{-3, \frac{5}{3}\right\}\]

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Home -> Solved problems -> Solve the quadratic equation by Completing the Square

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