Question

How do you solve `x^2 + 18x + 80 = 0` by completing the square?

Answer 1

I found:
`x_1=-8`
`x_2=-10`

Explanation:

Start by taking `80` to the right and get:
`x^2+18x=-80`
now you need a number that multiplied by `2` gives `18`...could be `9`!
So, add and subtract NOT `9` but `9^2=81`!
`x^2+18xcolor(red)(+81-81)=-80`
take `-81` to the right:
`x^2+18x+81=81-80`
so that you can write:
`(x+9)^2=1`
root square both sides:
`x+9=+-sqrt(1)=+-1`
So you get two solutions:
`x_1=-8`
`x_2=-10`

Answer 2

`x = -8`
or
`x=-10`

Explanation:

Given : `x^2+18x+80=0`

Complete the square:
`color(white)("XXXX")` `x^2+18x+(18/2)^2 - (18/2)^2 +80 = 0`
Simplify:
`color(white)("XXXX")` `x^2+18x+9^2 -81 + 80 = 0`
Write as a squared binomial:
`color(white)("XXXX")` `(x+9)^2 -1 = 0`
Move the constant to the right side
`color(white)("XXXX")` `(x+9)^2 = 1`
Take the square root
`color(white)("XXXX")` `x+9 = +-1`
Move constant to the right side
`color(white)("XXXX")` `x = -10` or `x= -8`