How do you solve the quadratic equation by completing the square: #r^2 + 14r = -13#?

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Answer 1 · 2015-07-16T08:26:37

The solutions for the equation are:
#color(blue)(r = -1 , r=-13#

#r^2 +14r = -13#

To write the Left Hand Side as a Perfect Square, we add 49 to both sides
#r^2 +14r +49 = -13+49#

#r^2 +14r +49 = 36#

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get
#(r+7)^2 = 36#

#r + 7 = sqrt36# or #r +7 = -sqrt36#

#r + 7 = 6# or #r +7 = -6#

#color(blue)(r = -1 or r=-13#