Question

Solve: $x^2-6x+2=0$

Answer 1

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

Lets compare with $a{x}^2+bx+c=0,a\ne 0$

$a=1,b=-6,c=2$

Roots of the Quadratic equation $a{x}^2+bx+c=0,a\ne 0$ are,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\Rightarrow x=\frac{-(-6)\pm \sqrt{(-6{)}^2-4(1\left)\right(2)}}{2\left(1\right)}$

$\Rightarrow x=\frac{6\pm \sqrt{36-8}}{2}$

$\Rightarrow x=\frac{6\pm \sqrt{28}}{2}$

$\Rightarrow x=\frac{6\pm \sqrt{4\times 7}}{2}$

$\Rightarrow x=\frac{6\pm 2\sqrt{7}}{2}$

$\Rightarrow x=\frac{2(3\pm \sqrt{7})}{2}$

$\therefore x=3\pm \sqrt{7}$