# Difference between revisions of "NSolve Command"

##### Command Categories (All commands)

NSolve[ <Equation> ]
Attempts (numerically) to find a solution for the equation for the main variable. For non-polynomials you should always specify a starting value (see below).
Example:
`NSolve[x^6 - 2x + 1 = 0]` yields {x = 0.51, x = 1}.

NSolve[ <Equation>, <Variable> ]
Attempts (numerically) to find a solution of the equation for the given unknown variable. For non-polynomials you should always specify a starting value (see below).
Example:
`NSolve[a^4 + 34a^3 = 34, a]` yields {a = -34.00086498588374, a = 0.9904738885574178}.

NSolve[ <Equation>, <Variable = starting value> ]
Finds numerically the list of solutions to the given equation for the given unknown variable with its starting value.
Examples:
• `NSolve[cos(x) = x, x = 0]` yields {x = 0.74}
• `NSolve[a^4 + 34a^3 = 34, a = 3]` yields {a = 0.99}.

NSolve[ <List of Equations>, <List of Variables> ]
Attempts (numerically) to find a solution of the set of equations for the given set of unknown variables.
Example:
`NSolve[{pi / x = cos(x - 2y), 2 y - pi = sin(x)}, {x = 3, y = 1.5}]` yields {x = 3.141592651686591, y = 1.570796327746508}.
Note:
• If you don't give a starting point like a=3 or {x = 3, y = 1.5} the numerical algorithm may find it hard to find a solution (and giving a starting point doesn't guarantee that a solution will be found)
• The number of decimals depends on the choosen in global rounding.
• NSolve won't work for functions that are asymptotic to the x-axis. They can often be reformulated though