Solve the following quadratic equations by completing the square. Express your answers in simplified exact form, including surds or fractions where necessary. Be prepared for fractions and more complex rearrangements!
Solve: $3x^2 - 10x + 6 = 0$
Solve: $-2x^2 + 7x - 4 = 0$
Solve: $x^2 + \frac{2}{3}x - \frac{1}{4} = 0$
Solve: $5x^2 - 11x + 3 = 0$
Solve: $ax^2 + bx + c = 0$ (Derive the quadratic formula)
Solve: $4x^2 - 9x + 2 = 0$
Solve: $x^2 - \sqrt{5}x + 1 = 0$
Solve: $(x+1)(x-5) = 1$
Solve: $\frac{1}{x-1} + \frac{1}{x+2} = 1$
Find the value(s) of $k$ for which the equation $x^2 + (k+2)x + k = 0$ has exactly one real solution.