How do you solve using the completing the square method #0=3x^2-2x-12#?

1 Answer
Jul 11, 2017

Answer:

#x=1/3+-sqrt37/3#

Explanation:

#"require the coefficient of " x^2" term to be unity"#

#rArr3(x^2-2/3x-4)=0#

#"to complete the square"#

add #(1/2"coefficient of the x-term")^2" to " x^2-2/3x#

#3(x^2-2/3xcolor(red)(+1/9)color(magenta)(-1/9)-4)=0#

#"we must also subtract " 1/9#

#rArr3((x-1/3)^2-37/9)=0#

#"distributing gives"#

#3(x-1/3)^2-37/3=0#

#rArr(x-1/3)^2=37/9#

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

#rArrx-1/3=+-sqrt(37/9)larr" note plus or minus"#

#"add "1/3" to both sides"#

#rArrx=1/3+-sqrt37/3#