Question 171868


{{{2a^2-46a+252=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{aa^2+ba+c}}} where {{{a=2}}}, {{{b=-46}}}, and {{{c=252}}}



Let's use the quadratic formula to solve for a



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



{{{a = (-(-46) +- sqrt( (-46)^2-4(2)(252) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=-46}}}, and {{{c=252}}}



{{{a = (46 +- sqrt( (-46)^2-4(2)(252) ))/(2(2))}}} Negate {{{-46}}} to get {{{46}}}. 



{{{a = (46 +- sqrt( 2116-4(2)(252) ))/(2(2))}}} Square {{{-46}}} to get {{{2116}}}. 



{{{a = (46 +- sqrt( 2116-2016 ))/(2(2))}}} Multiply {{{4(2)(252)}}} to get {{{2016}}}



{{{a = (46 +- sqrt( 100 ))/(2(2))}}} Subtract {{{2016}}} from {{{2116}}} to get {{{100}}}



{{{a = (46 +- sqrt( 100 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{a = (46 +- 10)/(4)}}} Take the square root of {{{100}}} to get {{{10}}}. 



{{{a = (46 + 10)/(4)}}} or {{{a = (46 - 10)/(4)}}} Break up the expression. 



{{{a = (56)/(4)}}} or {{{a =  (36)/(4)}}} Combine like terms. 



{{{a = 14}}} or {{{a = 9}}} Simplify. 



So the answers are {{{a = 14}}} or {{{a = 9}}}