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George has a quadratic of the form $x^2+bx+\frac13$, where $b$ is a specific negative number. Using his knowledge of how to complete the square, George is able to rewrite this quadratic in the form $(x+m)^2+\frac{1}{12}$. What is $b$?

Guest Jan 23, 2018

Best Answer 

 #1
avatar+7164 
+2

x2 + bx + 1/3

 

=   x2 + bx + (b/2)2 - (b/2)2 + 1/3

 

=  (x + b/2)2 - (b/2)2 + 1/3

 

Now we can see that...

 

-(b/2)2 + 1/3   =   1/12

 

-(b/2)2   =   1/12  - 1/3

 

-(b/2)2   =   -1/4

 

(b/2)2   =   1/4

 

b2/4   =   1/4

 

b2   =   1

 

b   =   ± 1

 

b  is a negative number, so   b = -1

hectictar  Jan 23, 2018
 #1
avatar+7164 
+2
Best Answer

x2 + bx + 1/3

 

=   x2 + bx + (b/2)2 - (b/2)2 + 1/3

 

=  (x + b/2)2 - (b/2)2 + 1/3

 

Now we can see that...

 

-(b/2)2 + 1/3   =   1/12

 

-(b/2)2   =   1/12  - 1/3

 

-(b/2)2   =   -1/4

 

(b/2)2   =   1/4

 

b2/4   =   1/4

 

b2   =   1

 

b   =   ± 1

 

b  is a negative number, so   b = -1

hectictar  Jan 23, 2018

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