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Solve 5x2 - 7x + 2 = 0 by completing the square.

What is the constant added on to form the perfect square trinomial?

49/4

49/25

49/100

 Jan 28, 2019
 #1
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5x^2 - 7x + 2 = 0

 

5x^2 - 7x   =  - 2         factor out 5

 

5 (x^2 - (7/5)x ) = -2       take (1/2) of (7/5) = 7/10....square it = 49/100...add and subract it within the parentheses 

 

5 ( x^2 - (7/5)x  + 49/100 - 49/100)  = -2    divide both sides by 5

 

 x^2 - (7/5)x + 49/100 -  49/100  =  - 2/5      add 49/100 to both sides

 

x^2 - (7/5)x + 49/100  = -2/5 + 49/100    factor the left side

 

(x - 7/10)^2  =  -40/100  + 49/100

 

(x - 7/10^2 =   9/100         take both roots

 

x -7 /10    =   ±√ (9/100)

 

x  -  7/10   =  ±3/10     add 7/10 to both sides

 

x = ±3/10 + 7/10

 

x =  3/10 + 7/10  = 1               or            x =   -3/10 + 7/10 =  4/10 = 2/5

 

49/100 is the added constant

 

 

cool cool  cool

 Jan 28, 2019

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