How do you solve #3x^2+5x=2# by completing the square?

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Answer 1 · 2018-06-26T10:15:03

#color(violet)(x = -2, 1/3#

#3x^2 + 5x = 2#

#(sqrt(3x))^2 + 2 * sqrt3 * x * (5/ (2 *sqrt3)) = 2#

#(sqrt3 x)^2 + 2 * sqrt3 * x * (5/ (2 *sqrt3)) + (5/(2 sqrt3))^2 = 2 + (5/(2 sqrt3))^2#

#((sqrt3 x) + 5/(2 sqrt3))^2 = 2 + 25/12 = 49/12#

#((sqrt3 x) + 5/(2 sqrt3))^2 = (sqrt(49/12))^2#

# sqrt 3 x + 5/ (2 sqrt3) = +- 7/ (2 sqrt3)#

#sqrt3 x = (-5 +- 7) / (2 sqrt3)#

#x = (-5 +- 7) / 6 = -2, 1/3#