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The other bracketing value is taken to be ''x''<sub>3</sub> if f(''x''<sub>3</sub>) has the opposite sign to f(''x''<sub>4</sub>), or otherwise whichever of ''x''<sub>1</sub> and ''x''<sub>2</sub> has f(x) of opposite sign to f(''x''<sub>4</sub>).
The method can be summarized by the formula <ref>{{Cite journal | last1 = Ridders | first1 = C. | doi = 10.1109/TCS.1979.1084580 | title = A new algorithm for computing a single root of a real continuous function | journal = IEEE Transactions on Circuits and Systems | volume = 26 | pages = 979–980| year = 1979 | pmid = | pmc = }}</ref>
:<math>x_3 = x_1 + (x_1 - x_0)\frac{\operatorname{sign}[f(x_0)]f(x_1)}{\sqrt{f(x_1)^2 - f(x_0)f(x_2)}} .</math>
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