Question

50 + x^2/20 + x/20=5x

Answer 1

Answer:  x = 87.582 , 11.148 .
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Explanation
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Given:
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   50 + (x²/20) + (x/20) = 5x ;  Solve for "x" ;
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  → First, let us multiply the entire equation (both sides) by "20" ; to get rid of the fractions ;
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  20 * {50 + (x²/20) + (x/20) = 5x } ;
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 to get: 
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1000 + x² + x = 100x ; 
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Subtract "x" from each side ;
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1000 + x² + x − x  = 100x  − x ; 

to get:  1000 + x² = 99x ; 

Rewrite as:

x² + 1000 = 99x ;

Subtract "99x" from each side of the equation:
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   x² + 1000 − 99x = 99x − 99x ;

to get: 

   x² − 99x + 1000 = 0 

This expression is written is "quadratic format" ; that is:
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   " ax² + bx + c  = 0 ;  a ≠ 0 " ;  
 
                in which:  a = 1 (implied coefficient of "1"; since anything                                                    multiplied by "1";  is that same value) ;

                               b = -99 ;
                                
                               c = 1000 ;
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       →  So, we can solve for "x" using the quadratic equation formula (since the expression cannot be factored):
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   x =   {- b ± √(b² − 4ac) } / {2a} ;
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Note:  - b =  - (-99) = 99 ;
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            b² = (-99)² = 9801 .
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         4ac = 4*a*c = 4*1*1000 = 4000 ;
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             (b² − 4ac)  = 9801 − 4000 = 5801
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           √ (b² − 4ac) =  √(5801) = 76.16429609731846
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            2a = 2*a = 2*1 = 2 
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Rewrite the quadratic formula:
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    x  =  { - b ± √(b² − 4ac) } / {2a}  ;
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    → x = (99 ± 76.16429609731846) / 2 ; 
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And, with the "±" ; we have 2 (TWO) potential solutions:
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Case 1)
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    →   x = (99  + 76.16429609731846) / 2 ;

             =  (175.16429609731846) / 2

             =  87.58214804865923 ;  →round to: 87.582 .
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Case 2)
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  →   x  =  (99 − 76.16429609731846) / 2 ;
 
            =   (22.83570390268154) / 2 ;
       
            =  11.41785195134077 ;  round to:  11.418.
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Answer:  x  =  87.582 , 11.148 .
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