Question

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

Answer 1

`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`