Question

Find the roots of the equations by the method of completing the square.
$x^2+7x-6=0$

Answer 1

$x^2+7x-6=0$

$\Rightarrow$ Here, $a=1,b=7,c=-6$

$\Rightarrow$ $x^2+7x=6$

Now, ${\left(\frac{b}{2}\right)}^2={\left(\frac{7}{2}\right)}^2=\frac{49}{4}$

Adding, $\frac{49}{4}$ on both sides,

$\Rightarrow$ $x^2+7x+\frac{49}{4}=6+\frac{49}{4}$

$\Rightarrow$ ${(x+\frac{7}{2})}^2=\frac{73}{4}$

$\Rightarrow$ $x+\frac{7}{2}=\pm \frac{\sqrt{73}}{2}$

$\Rightarrow$ $x+\frac{7}{2}=\frac{\sqrt{73}}{2}$ and $x+\frac{7}{2}=-\frac{\sqrt{73}}{2}$

$\Rightarrow$ $x=\frac{\sqrt{73}}{2}-\frac{7}{2}$ and $x=-\frac{\sqrt{73}}{2}-\frac{7}{2}$