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

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Answer 1 · 2018-07-09T02:34:40

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

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!

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