Question

How do you solve `x^2 - 4x = 5` by completing the square?

Answer 1

`x^2 - 4x = 5`
To write the Left Hand Side as a Perfect Square, we add 4 to both sides:

`x^2 - 4x + 4 = 5 + 4`

`x^2 -2.2.x + 2^2 = 9`
`x^2 -2.2.x + 2^2 = 3^2`

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

`x - 2 = sqrt9` or `x - 2 = -sqrt9`

`color(green)(x = sqrt 9 +2` or `color(green)(x = -sqrt 9 + 2`