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### Section 2-6 : Quadratic Equations - Part II

1. Complete the square on the following expression.

${x^2} + 8x$

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Start Solution

First, we need to identify the number we need to add to this. Recall that we will need the coefficient of the $$x$$ to do this. The number we need is,

${\left( {\frac{8}{2}} \right)^2} = {\left( 4 \right)^2} = 16$ Show Step 2

To complete the square all we need to do then is add this to the expression and factor the result. Doing this gives,

$\require{color}\require{bbox} \bbox[2pt,border:1px solid black]{{{x^2} + 8x \,{\color{Red} + 16} = {{\left( {x + 4} \right)}^2}}}$