```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 = (-(-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}}}

```