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Each solution to $x^2 + 5x + 8 = 0$ can be written in the form $x = a + b i,$ where $a$ and $b$ are real numbers. What is $a + b^2$?

 Feb 22, 2021
 #1
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x^2  + 5x  +  8  = 0     complete the square  on  x

 

x^2  +  5x    =    -8        take 1/2 of 5  = 5/2....square it  =  25/4.....add to both sides of the  equation

 

x^2  + 5x  + 25/4  =  -8  + 25/4     factor  the left....simplify the right

 

(x + 5/2) ^2   =  -32/4  + 25/4

 

( x + 5/2)^2  =  - 7/4      we  only need  one  root

 

x + 5/2  =   √7i /  2

 

x =  -5/2   + (√7/2) i

 

 

a  + b^2  =      -5/2  +  (√7/2)^2    =   -5/2  + 7/4  =    -10/4 + 7/4  =   -3/4

 

 

cool cool cool

 Feb 22, 2021

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