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# solve by completing the square

x^2-2x-8=0

x^2-14x-3=0

### 2 Answers by Expert Tutors

PAT T. | Every problem has a solution let's find it.Every problem has a solution let's find ...
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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

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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