The roots of $x^{2}+12x+36=0$ are ...........

State whether the following statements are true or false. Justify your answers.
$(i)$ Every quadratic equation has at most two roots.
$(ii)$ If the coefficient of $x^{2}$ and the constant term of a quadratic equation have opposite signs,then the quadratic equation has real roots.

If one of the roots of $x^{2}-2x-c=0$ is $5$,the other root is ...........

If the following quadratic equation has two equal and real roots,then find the value of $k$: $x^{2} - kx + 25 = 0$.

Solve the following equation using the method of factorization and write its solution set: $x - \frac{1}{x} - \frac{45}{14} = 0$; $x \neq 0$.

Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x-1} + \frac{x-2}{x+2} = 3$