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

Jul 9, 2018

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

Explanation:

We have the following:

${x}^{2} - 8 x + 20 = 0$, which is in standard form

$a {x}^{2} + b x + c = 0$

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

${x}^{2} - 8 x = - 20$

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

${x}^{2} - 8 x + 16 = - 20 + 16$

We can factor the left to get

${\left(x - 4\right)}^{2} = - 4$

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

$x - 4 = \sqrt{- 4}$

We can rewrite $\sqrt{- 4}$ as $\sqrt{- 1} \sqrt{4}$, which simplifies to $\pm 2 i$. We now have

$x - 4 = \pm 2 i$

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

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

Hope this helps!