(iii) Solve the Equation:
\[x^2 – 13x – 30 = 0\]
Solution:
Given: $x^2 – 13x – 30 = 0$
We need to find two numbers that multiply to -30 and add to -13. These are -15 and +2.
$\therefore x^2 – 15x + 2x – 30 = 0$
$\therefore x(x – 15) + 2(x – 15) = 0$
$\therefore (x – 15)(x + 2) = 0$
$\therefore x – 15 = 0 \quad \text{or} \quad x + 2 = 0$
$\therefore x = 15 \quad \text{or} \quad x = –2$