Find the roots of the quadratic equation $x^{2}+10x+7=0$ by using the method of completing the square.

We get $2$ litres of kerosene less in Rs. $360$ if the price of kerosene increases by Rs. $2$ per litre. Find the original price of kerosene per litre.

Solve the following quadratic equation using the quadratic formula,if the equation has a solution in $R$: $5x^{2} + 8x + 3 = 0$.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $x^{2}+\sqrt{2}x-4=0$; $x=-2\sqrt{2}$.

Represent the following situation in the form of a quadratic equation:
The area of a rectangular plot is $528 \ m^{2}$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Verify whether the given value of $x = \frac{-2}{m+n}$ is a solution of the quadratic equation $(m+n)^{2} x^{2} + (m+n) x - 2 = 0$ or not.