How do you solve #5x^2-10x=23# by completing the square?

1 Answer
May 21, 2018

Answer:

#x=1+-sqrt(28/5)#

Explanation:

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

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

#"factor out 5"#

#5(x^2-2x)=23#

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

#5(x^2+(-1)xcolor(red)(+1))=23color(red)(+5)larr"note"#

#rArr5(x-1)^2=28#

#rArr(x-1)^2=28/5#

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

#sqrt((x-1)^2)=+-sqrt(28/5)larrcolor(blue)"note plus or minus"#

#rArrx-1=+-sqrt(28/5)#

#"add 1 to both sides"#

#rArrx=1+-sqrt(28/5)larrcolor(red)"exact solutions"#