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Home / Algebra / Solving Equations and Inequalities / Quadratic Equations - Part II
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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,

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