Question
Solve the following equation by factorisation :
$2x^2 + ax – a^2= 0$
$2x^2 + ax – a^2= 0$
✓
Answer
$
\begin{aligned}
& 2 x^2+a x-a^2=0 \\
& \Rightarrow 2 x^2+2 a x-a x-a^2=0 \\
& \Rightarrow 2 x(x+a)-a(x+a)=0 \\
& \Rightarrow(x+a)(2 x-a)=0
\end{aligned}
$
Either $x+a=0$,
then $x=-a$
or
$2 x-a=0 \text {, }$
then $2 x = a$
$\Rightarrow x =\frac{a}{2}$
Hence $x =- a, \frac{a}{2}$.
\begin{aligned}
& 2 x^2+a x-a^2=0 \\
& \Rightarrow 2 x^2+2 a x-a x-a^2=0 \\
& \Rightarrow 2 x(x+a)-a(x+a)=0 \\
& \Rightarrow(x+a)(2 x-a)=0
\end{aligned}
$
Either $x+a=0$,
then $x=-a$
or
$2 x-a=0 \text {, }$
then $2 x = a$
$\Rightarrow x =\frac{a}{2}$
Hence $x =- a, \frac{a}{2}$.
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