Solve quadratic equation by completing the square. Express your answer as exact roots ?

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1 Answer
Jim G.
Mar 12, 2018

#x=-1+-sqrt6/3#

Explanation:

#"to "color(blue)"complete the square"#

#• " the coefficient of the "x^2" term must be 1"#

#rArr3(x^2+2x+1/3)=0#

#• " add/subtract "(1/2"coefficient of the x-term")^2" to"#
#x^2+2x#

#rArr3(x^2+2(1x)color(red)(+1)color(red)(-1)+1/3)=0#

#rArr3(x+1)^2+3(-1+1/3)=0#

#rArr3(x+1)^2-2=0#

#rArr(x+1)^2=2/3#

#color(blue)"take the square root of both sides"#

#rArrx+1=+-sqrt(2/3)larrcolor(blue)"note plus or minus"#

#rArrx=-1+-sqrt6/3larrcolor(blue)"rationalise denominator"#

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