Algebra

 

Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.  

 

combine like terms and   

arrange as ax² + bx + c                              x² + (k – 9) • x + 16    

 

For the quadratic to be the square of a binomial, the "b" term    

has to be twice the value of the square root of the "c" term.    

 

                            k – 9  =  (2)(+4)    ==>>    k  =  ( +8 + 9 )    

 

                            when  k = 17    ==>>   x² + (17 – 9) • x + 16  =  (x + 4)²    

                            when  k =   1    ==>>   x² + (  1 – 9) • x + 16  =  (x – 4)²    

 

   sum of both values of  k  =  18       

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