Question

Solve the following equation by using the method of completing the square:
$x^2-6x+3=0$

Answer 1

The given equation is $x^2-6x+3=0$

Now,

$x^2-6x+3=0$

$\Rightarrow x^2-6x=-3$

$\Rightarrow x^2-2\times x\times 3+3^2=-3+3^2$ [adding $3^2$ on both side]

$\Rightarrow (x-3{)}^2=6$ [Using algebraic identity : $a^2-2ab+b^2=(a-b{)}^2$]

$\Rightarrow x-3=\pm \sqrt{6}$

$\Rightarrow x=3\pm \sqrt{6}$

Hence, the solution is $x=(3+\sqrt{6})$ or $(3-\sqrt{6})$