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Masha has a quadratic of the form x^2 + bx + 1, where b is a specific positive number. Using her knowledge of how to complete the square, Masha is able to rewrite this quadratic in the form (x+m)^2 - 63. What is b?

 Dec 18, 2018
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Masha has a quadratic of the form x^2 + bx + 1, where b is a specific positive number. Using her knowledge of how to complete the square, Masha is able to rewrite this quadratic in the form (x+m)^2 - 63. What is b?

 

x^2 + bx  + b^2/4    + 1  - b^2/4

 

(x + b/2)^2 + 1 - b^2/4

 

And

 

(x + b/2)^2  -   63

 

This implies that

 

+1 - b^2/4  =  -63      rearrange as

 

64 = b^2/4        multiply both sides by 4

 

256 = b^2       take the positive root

 

16 = b       

 

 

cool cool cool

 Dec 18, 2018
edited by CPhill  Dec 19, 2018

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