Solve Quadratic Equation by Completing the Square - Search
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    Quadratic Equation Completing the Square Calculator - Symbolab

    Completing the Square: Solving Quadratic Equations - Purplemath
    Purplemath
    9.3: Solve Quadratic Equations by Completing the Square
    Mathematics LibreTexts
    Completing the Square - Math is Fun

    Say we have a simple expression like x2 + bx. Having xtwice in the same expression can make life hard. What can we do? Well, with a little inspiration from Geometry we can convert it, like this: As you can see x2 + bx can be rearranged nearlyinto a square ... ... and we can complete the square with (b/2)2 In Algebra it looks like this: So, by addin...

    Math is Fun

    Now ... we can't just add (b/2)2 without also subtractingit too! Otherwise the whole value changes. So let's see how to do it properly with an example: The result: x2 + 6x + 7 = (x+3)2− 2 And now xonly appears once, and our job is done!

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    Here is a method you may like, it is quick when you get used to it. First think about the result we want: (x+d)2+ e After expanding (x+d)2 we get: x2 + 2dx + d2+ e Now see if we can turn our example into that form to discover d and e. Now, let us look at a useful application: solving Quadratic Equations ...

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    We can complete the square to solve a Quadratic Equation(find where it is equal to zero). But a general Quadratic Equation may have a coefficient of a in front of x2: ax2+ bx + c = 0 To deal with that we divide the whole equation by "a" first, then carry on: x2+ (b/a)x + c/a = 0

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    Why complete the square when we can just use the Quadratic Formulato solve a Quadratic Equation? Just think of it as another tool in your mathematics toolbox.

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