Question 138577
I don't know how to slove anything.  But I will show you how to solve by completing the square.


{{{m^2-(1/2) m=7/2}}}


Step 1 is to put the constant term on the left, but that is already done.


Step 2: Divide the coefficient on the 1st degree term by 2, square the result, and then add that result to both sides of the equation.  {{{((-1/2)/2)^2=(-1/4)^2=1/16}}}, so:


{{{m^2-(1/2)m+1/16=7/2+1/16}}}
{{{m^2-(1/2)m+1/16=57/16}}}


Step 3: Factor the perfect square trinomial on the left:
{{{(m-1/4)^2=57/16}}}


Step 4: Take the square root of both sides, remembering to consider both the positive and negative root.


{{{m-1/4=sqrt(57/16)}}} or {{{m-1/4=-sqrt(57/16)}}}


Step 5: Add the opposite of the constant on the left to both sides:


{{{m=1/4+-sqrt(57/16)}}}


And finally simplify the radical:


{{{m=(1+-sqrt(57))/4}}}