One of the solutions of the quadratic equation $(x-3)^{2}-4=0$ is ..... .

Find the roots of the following quadratic equation by the method of completing the square: $4x^{2} + 4bx - (a^{2} - b^{2}) = 0$.

The faster train takes $1$ hour less than the slower train for covering a $400\, km$ distance. If the speed of the slower train is $20\, km/hr$ less than the speed of the faster train,find the speed of the slower train.

State whether the quadratic equation $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0$ has two distinct real roots. Justify your answer.

Find the roots of the quadratic equation $2x^{2}-\sqrt{5}x-2=0$ using the quadratic formula.

The value of discriminant $D$ for the equation $(3x - 14)^2 = 0$ is ........