Question

solve for x by completing the square
1. x^2 - mx - 6m^2 = 0
2. kx^2 + px + q = 0

Answer 1

\[\begin{align*}x^2-mx-6m^2&=0\\
x^2-mx+\frac{m^2}{4}-\frac{m^2}{4}&=6m^2\\
\left(x-\frac{m}{2}\right)^2&=6m^2+\frac{m^2}{4}\\
\left(x-\frac{m}{2}\right)^2&=\frac{23m^2}{4}\\
x-\frac{m}{2}&=\pm\sqrt{\frac{23m^2}{4}}\\
x&=\frac{m}{2}\pm\frac{\sqrt{23m^2}}{2}\\
\end{align*}\]