How do you solve the quadratic equation by completing the square: #x^2+8x-2=0#?

1 Answer
Jul 19, 2015

Answer:

#color(green)(x = sqrt 18 - 4# or # color(green)(x = -sqrt 18 -4#

Explanation:

#x^2 + 8x = 2#

To write the Left Hand Side as a Perfect Square, we add 16 to both sides.

#x^2 + 8x + 16 = 2 + 16#

#x^2 + 2*4*x + 4^2 = 18#

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get
#(x+4)^2 = 18#
#x + 4 = sqrt18# or #x +4 = -sqrt18#
#color(green)(x = sqrt 18 - 4# or # color(green)(x = -sqrt 18 -4#