Question 338326
{{{2y(y+8)=7(y+8)}}} Start with the given equation.



{{{2y^2+16y=7y+56}}} Distribute.



{{{2y^2+16y-7y-56=0}}} Get every term to the left side.



{{{2y^2+9y-56=0}}} Combine like terms.



Notice that the quadratic {{{2y^2+9y-56}}} is in the form of {{{Ay^2+By+C}}} where {{{A=2}}}, {{{B=9}}}, and {{{C=-56}}}



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



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



{{{y = (-(9) +- sqrt( (9)^2-4(2)(-56) ))/(2(2))}}} Plug in  {{{A=2}}}, {{{B=9}}}, and {{{C=-56}}}



{{{y = (-9 +- sqrt( 81-4(2)(-56) ))/(2(2))}}} Square {{{9}}} to get {{{81}}}. 



{{{y = (-9 +- sqrt( 81--448 ))/(2(2))}}} Multiply {{{4(2)(-56)}}} to get {{{-448}}}



{{{y = (-9 +- sqrt( 81+448 ))/(2(2))}}} Rewrite {{{sqrt(81--448)}}} as {{{sqrt(81+448)}}}



{{{y = (-9 +- sqrt( 529 ))/(2(2))}}} Add {{{81}}} to {{{448}}} to get {{{529}}}



{{{y = (-9 +- sqrt( 529 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{y = (-9 +- 23)/(4)}}} Take the square root of {{{529}}} to get {{{23}}}. 



{{{y = (-9 + 23)/(4)}}} or {{{y = (-9 - 23)/(4)}}} Break up the expression. 



{{{y = (14)/(4)}}} or {{{y =  (-32)/(4)}}} Combine like terms. 



{{{y = 7/2}}} or {{{y = -8}}} Simplify. 



So the solutions are {{{y = 7/2}}} or {{{y = -8}}}



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