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Which of the following equations correctly illustrates the Law of Cosines in order to solve for side $b$, where $a$, $b$, and $c$ are side lengths of the triangle?

$b^{2} = a^{2} - c^{2} - 2ac\cos{\beta}$

$b^{2} = a^{2} + c^{2} + 2ac\cos{\beta}$

$b^{2} = a^{2} + c^{2} - 2ac\cos{\beta}$

$b^{2} = a^{2} + c^{2} - 2ac\cos{\alpha}$