Question 74628

YOUR PROBLEM IS NOT CLEAR.
What does{{{(Xx2)}}}represent?  Is it {{{X^2}}} or is it {{{2X}}}?  I WILL ASSUME 2X

The area(A) of a rectangle equals Length(L) times Width(W)

Either 2X is the length and (X+9) is the width or visa versa--it makes no difference which we choose.  So our equation to solve is:

A=L*W

{{{352=2x(x+9)}}} get rid of parens

{{{352=2x^2+18x}}}  divide both sides by 2
{{{176=x^2+9x}}}  subtract 176 from both sides
{{{x^2+9x-176=176-176}}}

{{{x^2+9x-176=0}}}  quadratic in standard form
A=1
B=9
C=-176

We'll solve using the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-9 +- sqrt( 9^2-4*1*(-176) ))/(2*1) }}}  
{{{x = (-9 +- sqrt( 81+704))/(2)}}}  
{{{x = (-9 +- sqrt(785))/(2)}}} 
{{{x = (-9 +- 28.018)/(2)}}}  
{{{x = (-9 + 28.018)/(2)= 9.509}}} cm

{{{2x=2*9.509=19.018}}} cm------------------------------length
{{{(x+9)=9.509+9=18.509}}} cm-----------------------------width

We will discount the negative solution for x since lengths and widths are not negative numbers.

CK
A=L*W

352 sq cm=(19.018)(18.509)
352=~352


Hope this helps----ptaylor