How do you solve the quadratic equation by completing the square: #x^2+18x+67=0#?

1 Answer
Jul 19, 2015

Answer:

#color(green)(x = sqrt 14 -9# or # color(green)(x = -sqrt 14 -9#

Explanation:

#x^2 + 18x = -67#

To write the Left Hand Side as a Perfect Square, we add 81 to both sides.

#x^2 + 18x + 81 = -67 + 81#

#x^2 + 2*x*9 + 9^2 = 14#

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get
#(x+9)^2 = 14#
#x + 9 = sqrt14# or #x +9 = -sqrt14#

#color(green)(x = sqrt 14 -9# or # color(green)(x = -sqrt 14 -9#