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The quadratic \(x^2+1300x+1300\) can be written in the form \((x+b)^2+c\), where b and c are constants. What is \(\frac{c}{b}\)?

 Jul 15, 2019
 #1
avatar+102386 
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x^2  + 1300x  + 1300    complete the square on x

 

Take 1/2 of 1300 = 650.....square it  = 422500

Add it and subtract it

 

x^2  + 1300x  + 422500 + 1300 - 422500  

Factor the first three terms and simplify

 

(x + 650)^2  - 421200

 

c = - 421200     b  = 650

 

c  /  b   =    - 421200  / 650   =   -648

 

 

cool cool cool

 Jul 15, 2019

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