Question 207053
Two ways to do this:


Method #1


{{{m^2=7m}}} Start with the given equation.



{{{m^2-7m=0}}} Subtract 7m from both sides.



Notice that the quadratic {{{m^2-7m}}} is in the form of {{{Am^2+Bm+C}}} where {{{A=1}}}, {{{B=-7}}}, and {{{C=0}}}



Let's use the quadratic formula to solve for "m":



{{{m = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{m = (-(-7) +- sqrt( (-7)^2-4(1)(0) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-7}}}, and {{{C=0}}}



{{{m = (7 +- sqrt( (-7)^2-4(1)(0) ))/(2(1))}}} Negate {{{-7}}} to get {{{7}}}. 



{{{m = (7 +- sqrt( 49-4(1)(0) ))/(2(1))}}} Square {{{-7}}} to get {{{49}}}. 



{{{m = (7 +- sqrt( 49-0 ))/(2(1))}}} Multiply {{{4(1)(0)}}} to get {{{0}}}



{{{m = (7 +- sqrt( 49 ))/(2(1))}}} Subtract {{{0}}} from {{{49}}} to get {{{49}}}



{{{m = (7 +- sqrt( 49 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{m = (7 +- 7)/(2)}}} Take the square root of {{{49}}} to get {{{7}}}. 



{{{m = (7 + 7)/(2)}}} or {{{m = (7 - 7)/(2)}}} Break up the expression. 



{{{m = (14)/(2)}}} or {{{m =  (0)/(2)}}} Combine like terms. 



{{{m = 7}}} or {{{m = 0}}} Simplify. 



So the solutions are {{{m = 7}}} or {{{m = 0}}} 




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Or....


Method #2



{{{m^2=7m}}} Start with the given equation.



{{{m^2-7m=0}}} Subtract 7m from both sides.



{{{m(m-7)=0}}} Factor out the GCF 'm'



{{{m=0}}} or {{{m-7=0}}} Set each factor equal to zero.



{{{m=0}}} or {{{m=7}}} Solve for 'm' in each case.



So the solutions are {{{m=0}}} or {{{m=7}}} (note: the order of the solutions does not matter)