Question 315575
{{{(w+1)^2=2w^2+6w+5}}} Start with the given equation.



{{{w^2+2w+1=2w^2+6w+5}}} FOIL



{{{w^2+2w+1-2w^2-6w-5=0}}} Get every term to the left side.



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



Notice that the quadratic {{{-w^2-4w-4}}} is in the form of {{{Aw^2+Bw+C}}} where {{{A=-1}}}, {{{B=-4}}}, and {{{C=-4}}}



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



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



{{{w = (-(-4) +- sqrt( (-4)^2-4(-1)(-4) ))/(2(-1))}}} Plug in  {{{A=-1}}}, {{{B=-4}}}, and {{{C=-4}}}



{{{w = (4 +- sqrt( (-4)^2-4(-1)(-4) ))/(2(-1))}}} Negate {{{-4}}} to get {{{4}}}. 



{{{w = (4 +- sqrt( 16-4(-1)(-4) ))/(2(-1))}}} Square {{{-4}}} to get {{{16}}}. 



{{{w = (4 +- sqrt( 16-16 ))/(2(-1))}}} Multiply {{{4(-1)(-4)}}} to get {{{16}}}



{{{w = (4 +- sqrt( 0 ))/(2(-1))}}} Subtract {{{16}}} from {{{16}}} to get {{{0}}}



{{{w = (4 +- sqrt( 0 ))/(-2)}}} Multiply {{{2}}} and {{{-1}}} to get {{{-2}}}. 



{{{w = (4 +- 0)/(-2)}}} Take the square root of {{{0}}} to get {{{0}}}. 



{{{w = (4 + 0)/(-2)}}} or {{{w = (4 - 0)/(-2)}}} Break up the expression. 



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



{{{w = -2}}} or {{{w = -2}}} Simplify. 



So the only solution is {{{w = -2}}}