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Beginning Pre-Calculus for Game Developers by Boris Meltreger, John P. Flynt

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Completing the Square

Working with the basic form of the quadratic equation the previous section afforded, you gain some sense of what it is to complete the square of an expression to solve a quadratic equation. For starters, recall that these two equations represent standard forms of polynomials that incorporate squares:

(a + b)2 = a2 + 2ab + b2

(ab)2 = a2 – 2ab + b2

Generally, completing the square begins with examining an equation to discover whether you can rewrite it in a way that allows you to make a perfect square on the left side of the equal sign. To understand how this works, consider the following equation:

a2 – 6a – 12 = 0

This is a standard quadratic equation. To make it so that it represents the square of two expressions, you ...

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