Question

How do you solve `x^2+8x=20` using completing the square?

Answer 1

`(x+4)^2-16=20`

`(x+4)^2=36`

Square root both sides

`x+4=\pm6`

`x+4=6 or x+4=-6`

`x=2 or x=-10`

Answer 2

`x=2` and `x=-10`

Explanation:

When we complete the square, we want to take half of our `b` value, square it, and add it to the left side. Doing this, we get

`x^2+8x+color(blue)(16)=20+color(blue)(16)`

`16` is the value `(8/2)^2`. Notice, we add it to both sides to maintain the equality.

Our equation can be further simplified as

`(x+4)^2=36`

Taking the square root of both sides, we get

`x+4=6` and `x+4=-6`

Solving these equations gives us

`x=2` and `x=-10`

Hope this helps!