Question 236636


{{{4a^2-28a=-49}}} Start with the given equation.



{{{4a^2-28a+49=0}}} Add 49 to both sides.



Notice that the quadratic {{{4a^2-28a+49}}} is in the form of {{{Aa^2+Ba+C}}} where {{{A=4}}}, {{{B=-28}}}, and {{{C=49}}}



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



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



{{{a = (-(-28) +- sqrt( (-28)^2-4(4)(49) ))/(2(4))}}} Plug in  {{{A=4}}}, {{{B=-28}}}, and {{{C=49}}}



{{{a = (28 +- sqrt( (-28)^2-4(4)(49) ))/(2(4))}}} Negate {{{-28}}} to get {{{28}}}. 



{{{a = (28 +- sqrt( 784-4(4)(49) ))/(2(4))}}} Square {{{-28}}} to get {{{784}}}. 



{{{a = (28 +- sqrt( 784-784 ))/(2(4))}}} Multiply {{{4(4)(49)}}} to get {{{784}}}



{{{a = (28 +- sqrt( 0 ))/(2(4))}}} Subtract {{{784}}} from {{{784}}} to get {{{0}}}



{{{a = (28 +- sqrt( 0 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{a = (28 +- 0)/(8)}}} Take the square root of {{{0}}} to get {{{0}}}. 



{{{a = (28 + 0)/(8)}}} or {{{a = (28 - 0)/(8)}}} Break up the expression. 



{{{a = (28)/(8)}}} or {{{a =  (28)/(8)}}} Combine like terms. 



{{{a = 7/2}}} or {{{a = 7/2}}} Simplify. 



So the solution is {{{a = 7/2}}}