How do you solve x^2 + 8x = 14 by completing the square?

1 Answer
Apr 29, 2015

x^2 + 8x = 14

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

x^2 + 8x + 16 = 14 + 16

x^2 + 2*4*x + 4^2 = 30

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

(x+4)^2 = 30

x + 4 = sqrt30 or x +4 = -sqrt30

color(green)(x = sqrt 30 - 4 or color(green)(x = -sqrt 30 + 4