+0  
 
0
30
1
avatar+280 

Solve this quadratic by completing the square. \[x^2 + x + 1 = 0\]

 Jun 13, 2022
 #1
avatar+123309 
+2

Rearrange  as

 

x^2  + 1x  =   -1

 

Take (1/2)  of 1  = 1/2

Square it   = 1/4  and add to  both sides

 

x^2 + x  + 1/4   -1 +  1/4                 factor the left side and simplify the right

 

(x + 1/2)^2  =  -3/4                       take both roots

 

x + 1/2 =    ± sqrt (-3 )  / 2

 

x + 1/2  =   ± sqrt (3) i   /   2

 

x =   -1/2    ± sqrt (3) i  / 2

 

x =   [ -1  ±  sqrt (3) i  ]   /   2

 

 

cool cool cool

 Jun 13, 2022

5 Online Users

avatar