Question

Find the roots of the following quadratic equations (if they exist ) by the method of completing the square.
$3x^2+11x+10=0$

Answer 1

$3x^2+11x+10=0$

$x^2+\frac{11}{3}x+\frac{10}{3}=0$

$(x+\frac{11}{6}{)}^2-\frac{1}{36}=0$

$(x+\frac{11}{6}{)}^2-(\frac{1}{6}{)}^2=0$

$(x+\frac{11}{6}{)}^2=\frac{1}{6}$

$x+\frac{11}{6}=\frac{1}{6}$ $x+\frac{11}{6}=-\frac{1}{6}$

$x=\frac{1}{6}-\frac{11}{6}$ $x=-\frac{1}{6}-\frac{11}{6}$

$x=-\frac{10}{6}$ $x=-\frac{12}{6}$

$x=-\frac{5}{3}$ $x=-2$

$x=-\frac{5}{3},-2$