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avatar+229 

What is the sum of all values of $z$ such that $z^2=12z-7$?

 Feb 19, 2021
 #1
avatar+944 
+1

Let's rearrange the equation:\(z^2 - 12z + 7 = 0\)

 

This is a quadratic, so we can use the quadratic formula:

\(x = {12 \pm \sqrt{144-4 \cdot 1 \cdot (-7)} \over 2(1)} = \frac{12 \pm 2\sqrt{43}}{2} = 6 \pm \sqrt{43}\)

 Feb 19, 2021
 #2
avatar+118069 
+1

z^2  -  12z  +  7   =   0

 

We  have  the form   ax^2   + bx  +  c    =   0

 

The  sum  of  the  z  values  that solve this equation   =     -b / a   =    -(-12)  /  1   =    12

 

 

cool cool cool

 Feb 19, 2021

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