What do you need to add to complete the square for $x^{2} + 8 x$ $x^2+8x$ ?

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What do you need to add to complete the square for $x^{2} + 8 x$ $x^2+8x$ ?

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Answer 1 · 2018-04-01T21:36:03

16

Explanation:

Since the $8 x$ $8x$ is positive, the equation ${(x + y)}^{2}$ $(x+y)^2$ must have $y$ $y$ as a positive number. Let's see this!

An easy way to complete the square if you have the constants for $x^{2}$ $x^2$ and $x$ $x$ but not the non-variable number is to divide the $x$ $x$ constant, and then square it. Just like this:

$8 x$ $8x$ / $2$ $2$ $= 4$ $=4$ .
$4^{2} = 16$ $4^2=16$ .

The last number must be 16. Let's check it.

${(x + 4)}^{2} = x^{2} + 8 x + 16$ $(x+4)^2=x^2+8x+color(red)16$

The answer is $16$ $16$ .

Yay!

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What do you need to add to complete the square for $x^{2} + 8 x$ $x^2+8x$ ?

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What do you need to add to complete the square for $x^{2} + 8 x$ $x^2+8x$ ?