Question 325299
{{{w(w +4) = 621}}} Start with the given equation.



{{{w^2+4w = 621}}} Distribute.



{{{w^2+4w - 621=0}}} Subtract 621 from both sides.



Notice that the quadratic {{{w^2+4w-621}}} is in the form of {{{Aw^2+Bw+C}}} where {{{A=1}}}, {{{B=4}}}, and {{{C=-621}}}



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)(-621) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=4}}}, and {{{C=-621}}}



{{{w = (-4 +- sqrt( 16-4(1)(-621) ))/(2(1))}}} Square {{{4}}} to get {{{16}}}. 



{{{w = (-4 +- sqrt( 16--2484 ))/(2(1))}}} Multiply {{{4(1)(-621)}}} to get {{{-2484}}}



{{{w = (-4 +- sqrt( 16+2484 ))/(2(1))}}} Rewrite {{{sqrt(16--2484)}}} as {{{sqrt(16+2484)}}}



{{{w = (-4 +- sqrt( 2500 ))/(2(1))}}} Add {{{16}}} to {{{2484}}} to get {{{2500}}}



{{{w = (-4 +- sqrt( 2500 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{w = (-4 +- 50)/(2)}}} Take the square root of {{{2500}}} to get {{{50}}}. 



{{{w = (-4 + 50)/(2)}}} or {{{w = (-4 - 50)/(2)}}} Break up the expression. 



{{{w = (46)/(2)}}} or {{{w =  (-54)/(2)}}} Combine like terms. 



{{{w = 23}}} or {{{w = -27}}} Simplify. 



So the solutions are {{{w = 23}}} or {{{w = -27}}} 

  

Ignore the negative solution (since a negative width doesn't make sense) to find that the width is {{{w=23}}} meters.