solve by completeing the square

Question

m^2-9/2m=3/2

Answer 1

m^2 -9/2m = 3/2.
m^2 -9/2m + (9/4)^2 = 3/2 + (9/4)^2
m^2 - 9/2m +(9/4)^2 = 24/16 + 81/16
m^2 -9/2m + (9/4)^2 = 105/16
(m - 9/4)^2 = 105/16
Take sqrt of both sides:
m - 9/4 = (sqrt105)/4
m = 9/4 + (sqrt105)/4 = (9 +- sqrt105)/4
m = 4.8, and -0.31.