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The quadratic x^2-8x+1 can be written in the form ,(x+b)^2+c where b and c are constants. What is b+c?

 Mar 26, 2022
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x2 - 8x + 1

 

First:  separate the squared term and the single x-term from the constant:

         (x2 - 8x    ) + 1

Second:  complete the square by dividing the coefficient of the x-term by 2 and

                squaring the result:  -8 / 2  =  -4      (-4)2 = 16

Third:  add this result into the set of parentheses and subtract this result after the parentheses.

          (x2 - 8x + 16) + 1 - 16

Fourth:  factor the expression within the parentheses and simplify the constants:

          (x - 4)2 - 15

 

Can you take it from here?

 Mar 26, 2022

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