Question

Solve the following quadratic equation for x:
$x^2-4ax-b^2+4a^2=0$

Answer 1

$$\begin{gathered} x^2-4ax-b^2+4a^2=0 \\ \Rightarrow x^2-4ax+4a^2-b^2=0 \\ \Rightarrow {\left(x\right)}^2-2\left(2a\right)x+{\left(2a\right)}^2-{\left(b\right)}^2=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow {\left(x-2a\right)}^2-{\left(b\right)}^2=0 \\ \Rightarrow \left(x-2a-b\right)\left(x-2a+b\right)=0 \\ \Rightarrow x-2a-b=0\mathrm{or}x-2a+b=0 \\ \Rightarrow x=2a+b\mathrm{or}x=2a-b \end{gathered}$$