Question

Find the roots of the equation $3x^2+7x-20=0$ by the method of completing square?

Answer 1

$3x^2+7x-20=0$
$(\sqrt{3}x{)}^2+2(\sqrt{3}x)\left(\frac{7}{2\sqrt{3}}\right)+{\left(\frac{7}{2\sqrt{3}}\right)}^2-{\left(\frac{7}{2\sqrt{3}}\right)}^2-20=0$
${(\sqrt{3}x+\frac{7}{2\sqrt{3}})}^2-\frac{49}{12}-20=0$
${(\sqrt{3}x+\frac{7}{2\sqrt{3}})}^2-\left(\frac{49+240}{12}\right)=0$
${(\sqrt{3}x+\frac{7}{2\sqrt{3}})}^2-\frac{289}{12}=0$
${(\sqrt{3}x+\frac{7}{2\sqrt{3}})}^2-{\left(\frac{17}{\sqrt{12}}\right)}^2=0$
$(\sqrt{3}x+\frac{7}{2\sqrt{3}}+\frac{17}{\sqrt{12}})(\sqrt{3}x+\frac{7}{2\sqrt{3}}-\frac{17}{\sqrt{12}})=0$