SOLUTION: Determine the nature of the solutions of the equation 10t^2 - 8t = 0. 2) give exact and approximate solutions to thee decimal places x^2+2x+1=4 3) solve by copleting the square x

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Question 451144: Determine the nature of the solutions of the equation 10t^2 - 8t = 0.
2) give exact and approximate solutions to thee decimal places x^2+2x+1=4
3) solve by copleting the square x^2+13/2x=13
4) give exact and approximate solutions to three decimal places (x-5)^2=18
Thank you,
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

10t^2 - 8t = 0  2t(5t-4)=0    t = 0,.8   (2-real solutions)

x^2+2x+1=4 

x^2+2x-3=0   (x+3)(x-1)= 0    x = -3,1

x^2+13/2x=13

(x+13/4)^2 = 13 + 169/16 = 208/16 + 16*/169 = 377/16

 x + 13/4 = ± sqrt(377)/4

    x = -13/4 ± sqrt(377)/4  | x = -13/4 + sqrt(377/4),-13/4 - sqrt(377/4)



(x-5)^2=18

 x-5 = ± sqrt(18)= ± sqrt(9*2)= ± 3sqrt(2)

   x = 5 ± 3sqrt(2) | x = 5+3sqrt(2), 5-3sqrt(2) (exact solutions)

   x = 5 ±  4.243   | x = .757, 9.243   (approximate solutions)



x^2 + 1/2x = 13

 x(+1/4)^2 = 13 + 1/16 = 208/16 + 1/16 = 209/16

    x = -1/4 +sqrt(209)/4, -1/4-sqrt(209)/4