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-12x^2-x+7

 Feb 13, 2016
 #1
avatar+33659 
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What do you want to do with this?   It doesn't factor nicely, so perhaps you want to find the values of x that make the expression equal zero.  If so you could use the quadratic equation \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) or complete the square.

 

Set the expression equal to 0 and divide through by -12:  \(x^2 + \frac{x}{12}-\frac{7}{12}=0\)

 

Add \((\frac{1}{2\times12})^2 \rightarrow \frac{1}{576}\) to both sides and add 7/12 to both sides:

 

\(x^2+\frac{x}{12}+\frac{1}{288}=\frac{1}{576}+\frac{7}{12}\)   

 

The left hand side is now a perfect square and, since 7/12 = 376/576 we can write  \((x+\frac{1}{24})^2=\frac{337}{576}\)

 

 

Take the square root of both sides:   \(x=-\frac{1}{24}\pm\frac{\sqrt{337}}{24}\)

 

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 Feb 13, 2016
 #2
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-12x2-x+7=0

 

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\sqrt{}\)

 

x1= -0,81

x2=0,72

 Feb 13, 2016

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