Numerical methods

When an equation resists exact algebraic solving, numerical methods approximate the answer. The bisection method repeatedly halves an interval where a continuous function changes sign: for f(x) = x^2 - 2 on [1,2], since f(1) = -1 and f(2) = 2 have opposite signs, checking the midpoint 1.5 (f(1.5) = 0.25, positive) narrows the search to [1, 1.5], closing in on the true root, the square root of 2, about 1.41421.

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