The algebraic expressions guide showed how to factorise quadratic expressions such as \(2x^2 – 7x – 4\)

Solve \(2x^2 – 7x – 4 = 0\)

\(2x^2 – 7x – 4\) factorises as \((2x + 1)(x – 4)\).

\((2x + 1)(x – 4) = 0\).

\(2x + 1 = 0 \) means \(x = -\frac{1}{2}\).

\(x – 4 = 0\) means \(x = 4\). Therefore, \(x = -\frac{1}{2}\) or \(x = 4\).

Solve \(4x^2 – 169 = 0\)

\(4x^2 – 169 = (2x)^2 – (13)^2 = (2x + 13)(2x – 13)\)

So, \((2x + 13)(2x – 13) = 0\)

\(2x + 13 = 0 \) means \(x = \frac{-13}{2}\)

\(2x – 13 = 0 \) means \(x = \frac{13}{2}\).

\(x = = \frac{-13}{2}\) or \(= \frac{13}{2}\), which can be written as \(\pm\frac{13}{2}\) or \(\pm 6\frac{1}{2}\) or \(\pm 6.5\)

\(4x^2 – 169 = 0\)

\(4x^2 = 169\)

\(2x = \pm 13\)

\(x = \pm \frac{13}{2}\)