# `11x^2 -34x +3=0` by Completing Square (Question from Quadratic Equations)

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The equation `11x^2 - 34x + 3 = 0` has to be solved.

`11x^2 - 34x + 3 = 0`

=> `11x^2 - 2*sqrt 11*x*(17/sqrt 11) + 289/11 + 3 = 289/11`

=> `(sqrt 11*x - 17/sqrt 11)^2 = 256/11`

=> `sqrt 11*x - 17/sqrt 11 = +-16/sqrt 11`

=> `sqrt 11*x = +-16/sqrt 11 + 17/sqrt 11`

=> `x = +-16/11 + 17/11`

=> `x = 1/11` and x = 3

**The solution of the equation is x = `1/11` and x = 3**

`11x^2-34x+3=0`

`Delta=(34)^2-4(11)(3)=1156-132=1024>0`

Equation has 2 real different solutions:

`x=(34+-sqrt(1024))/22=(34+-32)/22=(17+-16)/11` `x_1=3` `x_2=1/11`