Question

How do you solve the quadratic equation by completing the square: `x^2-6x=0`?

Answer 1

`x^2-6 = 0`
`rArr x=0` or `x=6`
`color(white)("XXXX")`(by completing the square)

Explanation:

Given `x^2 - 6x = 0`

`color(white)("XXXX")`If `x^2` and `-6x` are the first two terms of a squared binomial:
`color(white)("XXXX")` `color(white)("XXXX")` `(x-a)^2 = (x^2 -2ax +a^2)`
`color(white)("XXXX")`Then (since `-2ax = -6ax`) `rArr a = 3`

`color(white)("XXXX")`and the third term must be `a^2 = 9`

`color(white)("XXXX")`So we need to add `9` (to both sides) to "complete the square"
`x^2-6x+9 = 9`

`color(white)("XXXX")`Rewriting as a squared binomial
`(x-3)^2 = 9`

`color(white)("XXXX")`Taking the square root of both sides
`x-3 = +-sqrt(9) = +-3`

`color(white)("XXXX")`Adding 3 to both sides
`x = 6` or `x = 0`

(Note that, in this case, the solution would be simpler to determine by factoring).