How do you solve using the completing the square method #2x^2 + 6x -5 =0 #?

1 Answer
Apr 15, 2018

Answer:

#x=-3/2+-1/2sqrt19#

Explanation:

#"using the method of "color(blue)"completing the square"#

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

#"factor out "2#

#rArr2(x^2+3x-5/2)=0#

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

#rArr2(x^2+2(3/2)xcolor(red)(+9/4)color(red)(-9/4)-5/2)=0#

#rArr2(x+3/2)^2+2(-9/4-5/2)=0#

#rArr2(x+3/2)^2-19/2=0#

#rArr2(x+3/2)^2=19/2#

#rArr(x+3/2)^2=19/4#

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

#sqrt((x+3/2)^2)=+-sqrt(19/4)larrcolor(blue)"note plus or minus"#

#rArrx+3/2=+-1/2sqrt19#

#rArrx=-3/2+-1/2sqrt19larrcolor(red)"exact solutions"#