Question

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

Answer 1

Solution:

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

Now divide the $x^2$ coefficient throughout,

$\Rightarrow x^2-\frac{5x}{3}+\frac{2}{3}$

Divide the coefficient of x by 2 and square it. Now add and subtract it in the LHS.

$\Rightarrow x^2-\frac{5x}{3}+\frac{2}{3}+\frac{25}{36}-\frac{25}{36}=0$

$\Rightarrow x^2-\frac{5x}{3}+\frac{25}{36}=\frac{1}{36}$

$\Rightarrow \frac{x-5}{6}=\pm \frac{1}{6}$

$\therefore \frac{x-5}{6}=\frac{1}{6}or\frac{x-5}{6}=\frac{-1}{6}$

$\Rightarrow x=1orx=\frac{2}{3}$