Question 600343


{{{2m^2+9m+7=3}}} Start with the given equation.



{{{2m^2+9m+7-3=0}}} Subtract 3 from both sides.



{{{2m^2+9m+4=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{am^2+bm+c}}} where {{{a=2}}}, {{{b=9}}}, and {{{c=4}}}



Let's use the quadratic formula to solve for m



{{{m = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{m = (-(9) +- sqrt( (9)^2-4(2)(4) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=9}}}, and {{{c=4}}}



{{{m = (-9 +- sqrt( 81-4(2)(4) ))/(2(2))}}} Square {{{9}}} to get {{{81}}}. 



{{{m = (-9 +- sqrt( 81-32 ))/(2(2))}}} Multiply {{{4(2)(4)}}} to get {{{32}}}



{{{m = (-9 +- sqrt( 49 ))/(2(2))}}} Subtract {{{32}}} from {{{81}}} to get {{{49}}}



{{{m = (-9 +- sqrt( 49 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{m = (-9 +- 7)/(4)}}} Take the square root of {{{49}}} to get {{{7}}}. 



{{{m = (-9 + 7)/(4)}}} or {{{m = (-9 - 7)/(4)}}} Break up the expression. 



{{{m = (-2)/(4)}}} or {{{m =  (-16)/(4)}}} Combine like terms. 



{{{m = -1/2}}} or {{{m = -4}}} Simplify. 



So the answers are {{{m = -1/2}}} or {{{m = -4}}}