Question 207875
{{{4(y-1)^2=8(y+1)}}} Start with the given equation.


 
{{{4(y^2-2y+1)=8(y+1)}}} FOIL



{{{4y^2-8y+4=8y+8}}} Distribute



{{{4y^2-8y+4-8y-8=0}}} Get every term to the left side.



{{{4y^2-16y-4=0}}} Combine like terms.



Notice that the quadratic {{{4y^2-16y-4}}} is in the form of {{{Ay^2+By+C}}} where {{{A=4}}}, {{{B=-16}}}, and {{{C=-4}}}



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



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



{{{y = (-(-16) +- sqrt( (-16)^2-4(4)(-4) ))/(2(4))}}} Plug in  {{{A=4}}}, {{{B=-16}}}, and {{{C=-4}}}



{{{y = (16 +- sqrt( (-16)^2-4(4)(-4) ))/(2(4))}}} Negate {{{-16}}} to get {{{16}}}. 



{{{y = (16 +- sqrt( 256-4(4)(-4) ))/(2(4))}}} Square {{{-16}}} to get {{{256}}}. 



{{{y = (16 +- sqrt( 256--64 ))/(2(4))}}} Multiply {{{4(4)(-4)}}} to get {{{-64}}}



{{{y = (16 +- sqrt( 256+64 ))/(2(4))}}} Rewrite {{{sqrt(256--64)}}} as {{{sqrt(256+64)}}}



{{{y = (16 +- sqrt( 320 ))/(2(4))}}} Add {{{256}}} to {{{64}}} to get {{{320}}}



{{{y = (16 +- sqrt( 320 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{y = (16 +- 8*sqrt(5))/(8)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{y = (16)/(8) +- (8*sqrt(5))/(8)}}} Break up the fraction.  



{{{y = 2 +- sqrt(5)}}} Reduce.  



{{{y = 2+sqrt(5)}}} or {{{y = 2-sqrt(5)}}} Break up the expression.  



So the solutions are {{{y = 2+sqrt(5)}}} or {{{y = 2-sqrt(5)}}} 



which approximate to {{{y=4.236}}} or {{{y=-0.236}}}