Question 321282
Solve by completing the square
m^2 - {{{25/2}}}m = {{{5/2}}}
:
m^2 - {{{25/2}}}m + ____ = {{{5/2}}}
:
Calculate the 3rd term to complete the square (25/4)^2 = 625/16
m^2 - {{{25/2}}}m + {{{625/16}}} = {{{5/2}}} + {{{625/16}}}
:
m^2 - {{{25/2}}}m + {{{625/16}}} = {{{40/16}}} + {{{625/16}}}
:
m^2 - {{{25/2}}}m + {{{625/16}}} = {{{665/16}}}
:
(m - {{{25/4}}})^2 = {{{665/16}}}
Find the square root of both sides
m - {{{25/4}}} = +/-{{{sqrt(665/16)}}}
Extract the fraction from the radical
m - {{{25/4}}} = +/-{{{(1/4)sqrt(665)}}}
Two solutions
m = {{{25/4}}} + {{{(1/4)sqrt(665)}}}
or
m = {{{(25 + sqrt(665))/4}}}
and
m = {{{(25 - sqrt(665))/4}}}