Solve the Quadratic Equation by Factorization: 2x² + ax − a² = 0

Question: Solve the following quadratic equation by factorization:

$$ 2x^2+ax-a^2=0 $$

Solution

$$ 2x^2+2ax-ax-a^2=0 $$

$$ 2x(x+a)-a(x+a)=0 $$

$$ (x+a)(2x-a)=0 $$

Either

$$ x+a=0 $$

$$ x=-a $$

or

$$ 2x-a=0 $$

$$ x=\frac{a}{2} $$

Hence,

$$ \boxed{x=-a,\ \frac{a}{2}} $$