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solve by completing the square

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2 Answers

 
X^2 - 2X - 8 = 0
 
a = 1  b = -2  c= -8
 
put in the form (x+b/2a)2 and keep the balance
 
(x-2/2)2-1 - 8 =0
 
(x - 1)2=9 
 
x- 1 = 3  or x -1 = -3
 
x = 3 + 1  or x = -3 + 1 
 
x  = 4, x = -2
 
previous solution is correct hopefully this explained where the added 1 came from and how to determine what constant to use to keep the balance of the equation.
 
x^2-14x-3=0
a = 1   b = -14
(x-14/2)=x2-14x +49
since you added 49 on the left then add to the right to keep the balance
(x - 7)² =0 + 49 + 3 = 52
x - 7 = √52
x = 7 + √52  or 7 - √52
 
 
 
X^2 - 2X - 8 = 0
 
X^2 -2X +1 -1 -8 = 0
 
X^2 - 2X + 1 = 9
 
( X - 1 ) ^2 = 9
 
X - 1  =  ± √9  = ±3
 
 X = 1 +3     X = 1 - 3
 
   X = -2, 4
 
 You should follow the same procedure and do it yourself.
 
 First step is add +49, -49 to the equation