Question 506871
{{{(w+2)^2=2w^2+10w+13}}}


{{{w^2+4w+4=2w^2+10w+13}}}



{{{w^2+4w+4-2w^2-10w-13=0}}} Get every term to the left side.



{{{-w^2-6w-9=0}}} Combine like terms.



Notice that the quadratic {{{-w^2-6w-9}}} is in the form of {{{Aw^2+Bw+C}}} where {{{A=-1}}}, {{{B=-6}}}, and {{{C=-9}}}



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



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



{{{w = (-(-6) +- sqrt( (-6)^2-4(-1)(-9) ))/(2(-1))}}} Plug in  {{{A=-1}}}, {{{B=-6}}}, and {{{C=-9}}}



{{{w = (6 +- sqrt( (-6)^2-4(-1)(-9) ))/(2(-1))}}} Negate {{{-6}}} to get {{{6}}}. 



{{{w = (6 +- sqrt( 36-4(-1)(-9) ))/(2(-1))}}} Square {{{-6}}} to get {{{36}}}. 



{{{w = (6 +- sqrt( 36-36 ))/(2(-1))}}} Multiply {{{4(-1)(-9)}}} to get {{{36}}}



{{{w = (6 +- sqrt( 0 ))/(2(-1))}}} Subtract {{{36}}} from {{{36}}} to get {{{0}}}



{{{w = (6 +- sqrt( 0 ))/(-2)}}} Multiply {{{2}}} and {{{-1}}} to get {{{-2}}}. 



{{{w = (6 +- 0)/(-2)}}} Take the square root of {{{0}}} to get {{{0}}}. 



{{{w = (6 + 0)/(-2)}}} or {{{w = (6 - 0)/(-2)}}} Break up the expression. 



{{{w = (6)/(-2)}}} or {{{w =  (6)/(-2)}}} Combine like terms. 



{{{w = -3}}} or {{{w = -3}}} Simplify. 



So the only solution is {{{w = -3}}}