2.16: Completing the square and a substitution equation

Given that $y = 2x^{2} - 4x - 7$, write $y$ in the form $a(x - b)^{2} + c$, where $a$, $b$ and $c$ are constants.

Hence write down the minimum value of $y$ and the value of $x$ at which it occurs.

Using your answer to part (i), solve the equation $2p - 4\sqrt{p} - 7 = 0$, giving your answer correct to $2$ decimal places.