Question 1009425
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Solve this quadratic equation for the unknown value of the width w

w*(w+6) = 23,

which is the same as 

{{{w^2 + 6w - 23}}} = {{{0}}}.

Use the quadratic formula. You will get

{{{w[1,2]}}} = {{{(-6 +- sqrt(6^2 +4*23))/2}}} = {{{(-6 +- sqrt(128))/2}}} = {{{(-6 +- 8*sqrt(2))/2}}} = {{{-3 +- 4*sqrt(2)}}}.

The negative root doesn't fit the condition.

Hence, w = {{{4*sqrt(2) - 3}}} is the unique solution.
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