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

1 Answer
Jim G.
Jun 8, 2018

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

Explanation:

#"to solve by "color(blue)"completing the square"#

#"add 15 to both sides"#

#2x^2-7x=15#

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

#"divide all terms by 2"#

#x^2-7/2x=15/2#

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

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

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

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

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

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

#x=7/4-13/4=-3/2#

#"or "x=7/4+13/4=5#

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