Question
Solve : x² + 8x - 48 = 0
✓
Answer
Method I : Completing the square.
$\begin{array}{l}
x^2+8 x-48=0 \\
\therefore x^2+8 x+16-16-48=0 \\
\therefore(x+4)^2-64=0 \\
\therefore(x+4)^2=64 \\
\therefore x+4=8 \text { or } x+4=-8 \\
\therefore x=4 \text { or } x=-12
\end{array}$
Method II : Factorisation
$\begin{array}{l}
x^2+8 x-48=0 \\
\therefore x^2+12 x-4 x-48=0 \\
\therefore x(x+12)-4(x+12)=0 \\
\therefore(x+12)(x-4)=0 \\
\therefore x+12=0 \text { or } x-4=0 \\
\therefore x=-12 \text { or } x=4
\end{array}$
$\begin{array}{l}
x^2+8 x-48=0 \\
\therefore x^2+8 x+16-16-48=0 \\
\therefore(x+4)^2-64=0 \\
\therefore(x+4)^2=64 \\
\therefore x+4=8 \text { or } x+4=-8 \\
\therefore x=4 \text { or } x=-12
\end{array}$
Method II : Factorisation
$\begin{array}{l}
x^2+8 x-48=0 \\
\therefore x^2+12 x-4 x-48=0 \\
\therefore x(x+12)-4(x+12)=0 \\
\therefore(x+12)(x-4)=0 \\
\therefore x+12=0 \text { or } x-4=0 \\
\therefore x=-12 \text { or } x=4
\end{array}$
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