We have a quadratic expression:
[tex]m^2-\frac{49}{2}m=\frac{1}{2}[/tex]We can rearrange and complete the square as:
[tex]\begin{gathered} m^2-\frac{49}{2}m=\frac{1}{2} \\ m^2-\frac{49}{2}m-\frac{1}{2}=0 \\ m^2-2\cdot\frac{49}{4}m+(\frac{49}{4})^2-(\frac{49}{4})^2-\frac{1}{2}=0 \\ (m-\frac{49}{4})^2-\frac{2401}{16}-\frac{8}{16}=0 \\ (m-\frac{49}{4})^2-\frac{2409}{16}=0 \\ (m-\frac{49}{4})^2=\frac{2409}{16} \\ m-\frac{49}{4}=\pm\sqrt{\frac{2409}{16}} \\ m=\frac{49}{4}\pm\frac{\sqrt{2409}}{4} \end{gathered}[/tex]Answer: m = 49/4 ± √2409/4
