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

Divide $29$ into two parts such that the sum of their squares is $425$.

State whether the quadratic equation $(x-1)(x+2)+2=0$ has two distinct real roots. Justify your answer.

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.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 11x + 10 = 0$

Examine whether the following equation is quadratic or not: $x^{3}-4x^{2}-x+1=(x-2)^{3}$