solve by completing the square

Question

x^2-2x-8=0

 

x^2-14x-3=0

Answer 1

 

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)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

 

 

 

Answer 2

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