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Use completion of squares to determine the solution of 3x^2 + 6x + 2 = 0

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tonyah995 | Student, Undergraduate | Salutatorian

Posted September 12, 2013 at 12:24 PM via web

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Use completion of squares to determine the solution of 3x^2 + 6x + 2 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 12, 2013 at 12:29 PM (Answer #1)

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The equation 3x^2 + 6x + 2 = 0 has to be solved.

3x^2 + 6x + 2 = 0

=> `(sqrt3*x)^2 + 2*sqrt3*sqrt 3*x + 2 = 0`

=> `(sqrt3*x)^2 + 2*sqrt3*sqrt 3*x + (sqrt 3)^2 + 2 = (sqrt 3)^2`

=> `(sqrt3*x)^2 + 2*sqrt3*sqrt 3*x + (sqrt 3)^2 = 3 - 2`

=> `(sqrt 3*x + sqrt 3)^2 = 1`

=> `sqrt 3*x + sqrt 3 = +-1`

=> `x = (+-1 - sqrt 3)/sqrt 3`

=> `x = +-1/sqrt 3 - 1`

The roots of `3x^2 + 6x + 2 = 0` are `+-1/sqrt 3 - 1`

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