Solve the following equation using the method of factorization: $x^{2} - 7 = 0$.

The speed of a motorboat in still water is $9\,km/h$. In a river,it covers $12\,km$ downstream and the same distance upstream in a total time of $3\,hours$. Find the speed of the current of the river. (The speed of the current of the river is less than the speed of the motorboat in still water.) (in $,km/h$)

The perimeter of a bigger square is $12\,m$ more than the perimeter of a smaller square. Three times the area of the smaller square is $11\,m^2$ more than the area of the bigger square. Find the length of the side of the bigger square.

The price of corn oil is ₹ $x$ per $kg$. If the price of corn oil is decreased by ₹ $10$ per $kg$,then how many kilograms of corn oil can be obtained for ₹ $500$ at the new rate?

Find the roots of the following quadratic equation by the method of completing the square: $16 x^{2}-24 x-1=0$

Obtain the roots of the following equation using the method of 'completing the square': $16x^{2} - 24x - 1 = 0$.