Solve 2x² - 2√2 x + 1 = 0. Give the root to two decimal places.

To solve by factorisation, find $p$ and $q$ with $p + q = b$ and $p \times q = a \times c$, split $bx$ into $px + qx$, and group. If a product is $0$, one factor is $0$. Never divide both sides by $x$, and check each root. The same method works when the numbers are surds: look for a perfect square, since $2 = \sqrt{2} \times \sqrt{2}$.