How do you solve using the completing the square method #2x^2 - 7x - 15 = 0#?

1 Answer
Mar 30, 2018

Answer:

#x=-3/2" or "x=5#

Explanation:

#"to use the method of "color(blue)"completing the square"#

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

#rArr2(x^2-7/2x-15/2)=0#

#• " add/subtract "(1/2"coefficient of the x-term")^2" to"#
#x^2-7/2x#

#2(x^2+2(-7/4)xcolor(red)(+49/16)color(red)(-49/16)-15/2)=0#

#rArr2(x-7/4)^2+2(-49/16-15/2)=0#

#rArr2(x-7/4)^2-169/8=0#

#rArr2(x-7/4)^2=169/8#

#rArr(x-7/4)^2=169/16#

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

#rArrx-7/4=+-sqrt(169/16)larrcolor(blue)"note plus or minus"#

#rArrx=7/4+-13/4#

#rArrx=7/4-13/4=-3/2" or "x=7/4+13/4=5#