Question 3289
You are certainly correct so far. You have {{{W(2W-10) = 2800}}}. To finish this, complete the multiplication on the right-hand side {{{2W^2 - 10W = 2800}}}. Now subtract 2800 from both sides to get {{{2W^2 - 10W - 2800 = 0}}}. We can factor this a little further to get {{{2(W^2 - 5W - 1400) = 0}}}. Now, you either have to be very observant or you have to know the quadratic formula. The quadratic formula tells us that the solution to this equation is:<br>
{{{(-b +- sqrt(b^2-4*a*c))/(2*a)}}}<br>
The values for a, b and c are 1, -5 and -1400 respectively. This gives solutions at:<br>
{{{(5 +- sqrt(25+5600))/2}}}<br>
The square root of 5625 is 75, so the solutions for this equation are 40 and -35. Well, you can't have a width of -35, so the width must be 40 and the length must be 70.