Question

Solve by completing the square. m^2-49/2m=1/2

Answer 1

We have a quadratic expression:

`m^2-(49)/(2)m=(1)/(2)`

We can rearrange and complete the square as:

`\begin{gathered} m^2-(49)/(2)m=(1)/(2) \\ m^2-(49)/(2)m-(1)/(2)=0 \\ m^2-2\cdot(49)/(4)m+((49)/(4))^2-((49)/(4))^2-(1)/(2)=0 \\ (m-(49)/(4))^2-(2401)/(16)-(8)/(16)=0 \\ (m-(49)/(4))^2-(2409)/(16)=0 \\ (m-(49)/(4))^2=(2409)/(16) \\ m-(49)/(4)=\pm\sqrt{(2409)/(16)} \\ m=(49)/(4)\pm(√(2409))/(4) \end{gathered}`

Answer: m = 49/4 ± √2409/4