How do you solve #c^2 + 8c + 2 = 5c + 15# by completing the square?

2 Answers
Apr 25, 2018

Answer:

See the Explanation:

Explanation:

#c^2 + 8c + 2 = 5c + 15#
#c^2 + 3c = 13#
#c^2 + 2(3/2)c = 13#
#c^2 + 2(3/2)c + (3/2)^2 - (3/2)^2 = 13#
#(c + 3/2)^2 - (3/2)^2 = 13#
#(c + 3/2)^2 = 13 + 9/4#
#c + 3/2 = +- sqrt(13 + 9/4)#
#c = -3/2 +- sqrt61/2#

Apr 25, 2018

Answer:

#c=-3/2+-1/2sqrt61#

Explanation:

#"rearrange equation into "color(blue)"standard form"#

#"subtract "5c+15" from both sides"#

#rArrc^2+3c-13=0larrcolor(blue)"in standard form"#

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

#• " the coefficient of the "c^2" term must be 1 which it is"#

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

#c^2+2(3/2)c color(red)(+9/4)color(red)(-9/4)-13=0#

#rArr(c+3/2)^2-61/4=0#

#rArr(c+3/2)^2=61/4#

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

#rArrc+3/2=+-sqrt(61/4)larrcolor(blue)"note plus or minus"#

#rArrc+3/2=+-1/2sqrt61#

#"subtract "3/2" from both sides"#

#rArrc=-3/2+-1/2sqrt61larrcolor(red)"exact solutions"#