Question

How do you convert `f(x)=x^2-8x+20` by completing the square?

Answer 1

`x=2i+4` and `x=-2i+4`

Explanation:

We have the following:

`x^2-8x+20=0`, which is in standard form

`ax^2+bx+c=0`

Let's subtract `20` from both sides to get

`x^2-8x=-20`

Let's take half of our `b` value square it, and add it to both sides. We now have the following:

`x^2-8x+16=-20+16`

We can factor the left to get

`(x-4)^2=-4`

Let's take the square root of both sides to get

`x-4=sqrt(-4)`

We can rewrite `sqrt(-4)` as `sqrt(-1)sqrt4`, which simplifies to `+-2i`. We now have

`x-4=+-2i`

To solve for `x`, add `4` to both sides to get

`x=2i+4` and `x=-2i+4`

Hope this helps!