Respuesta :

Answer:  x = 4.87 .
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   A = L * w  ;

(Area = Length * width ) 
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 Given:  Area = 288 in² .
           
            Length = (2x + 10) in
            
            Width =  (3x)  in 
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         A = L * w   ;
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  288 =  (2x + 10) * (3x) ; 
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Solve for "x" ;
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  Write as:
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(3x)*(2x + 10) = 288 ;
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  Note the distributive property of multiplication:
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  a(b+c) = ab + ac ; and:
  
  a(b−c) =  ab − ac ; 
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So; 
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  (3x)*(2x + 10) =
  
   (3x)*(2x)  +  (3x)*(10)  =
  
    6x²  +  30x = 288 ;
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Subtract "288" from each side of the equation:
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    6x²  +  30x − 288 = 288 − 288 ;
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    6x²  +  30x − 288 = 0 ;
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 Now, divide the ENTIRE equation by "6";
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    {6x²  +  30x − 288} / 6  = 0 / 6 ;
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      x²  +  5x − 48 = 0 ; 
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We can solve for "x" using the quadratic formula; 
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 Note, this equation:
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      x²  +  5x − 48 = 0 ;  is written is "quadratic format"; that is:
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  ax² + bx + c = 0 ; a ≠ 0 ;

in which:
             a = 1 (the implied coefficient of "1", since anything multiplied by                              "1" is that same value);
              b = 5 ; 
              c = -48 ;
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and we can solve for "x" using the quadratic equation formula; which is:
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             x =  { -b ± √(b² − 4ac) } / {2a} ;  a ≠ 0 ;
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So, we can plug in the values: 
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        First, let's simplify: "(b² − 4ac)" ; which is: 

                        5² − 4*1*(-48) = 25 − (-192) = 25 + 192 = 217 ;
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 So, x = -5  ± √(217) / (2*1) ;
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       x = { -5  ± √(217) } / 2 ;

So, there are 2 (TWO) values:
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Start with: 
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 x =  { -5 + √(217) } / 2  = 4.8654599313281177


then, { -5 − √(217) } / 2 = -19.7309198626562354
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Since we are dealing with a rectangle, the answer is the positive value; that is:  4.8654599313281177 ;  the question asks to round to the nearest hundredth, if necessary; so;  →  4.87 = x .
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