Question

How do you solve `5x^2 – 100x + 455 = 0` by completing the square?

Answer 1

`x=7`
or
`x=13`

Explanation:

`5x^2-100x+455=0`

First simplify by dividing both sides by 5
`color(white)("XXXX")` `x^2-20x+91=0`

If `(x^2-20x)` are the first two terms of a spared binomial the third term must be `(+100)`
`color(white)("XXXX")` `color(white)("XXXX")`since `(x-a)^2 = x^2-2ax+a^2`

Completing the square
`color(white)("XXXX")` `x^2-20x+100 -9 = 0`

`color(white)("XXXX")` `(x-10)^2 = 9`

Taking the square root of both sides
`color(white)("XXXX")` `x-10 = +-sqrt(9) = +-3`

`color(white)("XXXX")`x=7`or`x=13#