Solve by completing the square?

#9x^2-12x+5=0#

This does include the usage of imagery numbers.

1 Answer
Jim G.
Jun 18, 2018

#x=2/3+-1/3i#

Explanation:

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

#"divide through by 9"#

#x^2-4/3x+5/9=0#

#x^2-4/3x=-5/9#

#"add "(1/2"coefficient of x-term")^2" to both sides"#

#x^2+2(-2/3)x color(red)(+4/9)=-5/9color(red)(+4/9)#

#(x-2/3)^2=-1/9#

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

#sqrt((x-2/3)^2)=+-sqrt(-1/9)#

#x-2/3=+-1/3i#

#"add "2/3" to both sides"#

#x=2/3+-1/3i#

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