Question

Solve the equation $3x^2-5x+2=0$ by completing the square method.

Answer 1

Completing square method:

$3x^2-5x+2=0$

The given equation is not in the form to apply the method of completing squares. The coefficient of $x^2$ is not$1$.

To make the coefficient$1$, we need to divide the whole equation by $3$.

$x^2–\frac{5}{3}x+\frac{2}{3}=0$

Subtract and Add$\frac{25}{36}$both sides,

$\Rightarrow$$x^2–\frac{5}{3}x+\frac{25}{36}=\frac{25}{36}-\frac{2}{3}$

$\Rightarrow$ ${\left(x–\frac{5}{6}\right)}^2=\frac{25-24}{36}$

$\Rightarrow$ ${\left(x–\frac{5}{6}\right)}^2=\frac{1}{36}$

$\Rightarrow$ $\left(x–\frac{5}{6}\right)=\pm \sqrt{\frac{1}{36}}$

$\Rightarrow$ $\left(x–\frac{5}{6}\right)=\pm \frac{1}{6}$

Taking $+vesign$

$\left(x–\frac{5}{6}\right)=\frac{1}{6}\Rightarrow x=\frac{1}{6}+\frac{5}{6}\Rightarrow x=\frac{1+5}{6}\Rightarrow x=\frac{6}{6}\Rightarrow x=1$

Taking $-vesign$

$\left(x–\frac{5}{6}\right)=-\frac{1}{6}\Rightarrow x=-\frac{1}{6}+\frac{5}{6}\Rightarrow x=\frac{-1+5}{6}\Rightarrow x=\frac{4}{6}\Rightarrow x=\frac{2}{3}$

Hence,the roots of the equation are $x=1andx=\frac{2}{3}$.