`NSolve`¶

Numeric equation solver.

$ wo 'NSolve[x^2 - 2 == 0, x]'
{{x -> -1.4142135623730951}, {x -> 1.414213562373095}}

A bare polynomial stands for the equation poly == 0:

$ wo 'NSolve[x^2 - 2, x]'
{{x -> -1.4142135623730951}, {x -> 1.414213562373095}}

A cubic with machine-real coefficients has one real root and a conjugate pair:

$ wo 'Round[x /. NSolve[x^3 + 1.5 x^2 - 3.2 x + 4.7 == 0, x], 1/10^6]'
{-19079/6250, 2426/3125 - (120997*I)/125000, 2426/3125 + (120997*I)/125000}

A repeated root is listed once per multiplicity:

$ wo 'NSolve[x^3 - 4. x^2 == 0, x]'
{{x -> 0.}, {x -> 0.}, {x -> 4.}}

The variable may be left out, as with Solve:

$ wo 'NSolve[x^2 == 2]'
\{\{x -> -1\.414213562373095\d?\}, \{x -> 1\.414213562373095\d?\}\} (regex)

Constraints narrow the answer to the root inside them:

$ wo 'NSolve[1 == f^2 (3 - f) && 0 <= f <= 1]'
{{f -> 0.6527036446661393}}

NSolve¶