Question

Solve the equations by completing the square
$x^2+7x-6=0$

Answer 1

$x^2+7x-6=0\Rightarrow x^2+2.\frac{7}{2}x+{\left(\frac{7}{2}\right)}^2-6-\frac{49}{4}=0.$

${(x+\frac{7}{2})}^2-\frac{73}{4}=0.$

${(x+\frac{7}{2})}^2-{\left(\frac{\sqrt{73}}{2}\right)}^2=0\Rightarrow (x+\frac{7+\sqrt{73}}{2})(x+\frac{7-\sqrt{73}}{2})=0$

$\therefore x=-\left(\frac{7+\sqrt{73}}{2}\right)$ or, $x=-\left(\frac{7-\sqrt{73}}{2}\right)$