Question

Find the roots by method of completing the square: $3x^2$ – 7x – 20 = 0.

Answer 1

$3x^2-7x-20=0$
$x^2-\frac{7}{3}x-\frac{20}{3}=0$ (Dividing by 3 on both sides)
$\underset{}{x^2-\frac{7}{3}x+{\left(\frac{7}{6}\right)}^2}-{\left(\frac{7}{6}\right)}^2-\frac{20}{3}=0$
${(x-\frac{7}{6})}^2-{\left(\frac{7}{6}\right)}^2-\frac{20}{3}=0$
${(x-\frac{7}{6})}^2=\frac{4a}{36}+\frac{20}{3}$
${(x-\frac{7}{6})}^2=\frac{4a+240}{36}$
$x-\frac{7}{6}=\pm \sqrt{\frac{284}{36}}$
$x-\frac{7}{6}=+\frac{17}{6}x-\frac{7}{6}=-\frac{17}{6}$
$x=\frac{24}{6}=4x=-\frac{10}{6}=-\frac{5}{3}$