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Equation Solver
Equation Solver
Enter your values below and press Calculate to see your result instantly.
Use JS math syntax: x*x, Math.pow(x, 2), Math.cos(x). Solver finds roots where y=0.
The Discovered Root (x)
2.0000
ITERATIONS
4
CONVERGENCE
Absolute
The solver converged to x = 2 after 4 iterations using the Newton-Raphson approximation.
About the Equation Solver
Find a root of an equation f(x) = 0 numerically. Type the equation as an expression in x and give a starting guess.
How to use the Equation Solver
- Enter the Target Equation f(x) = 0 using JavaScript syntax, for example
Math.pow(x, 2) - 10orMath.sin(x). - Enter a Guess / Starting X and choose the Precision (Tolerance).
- Press Find Roots.
Formula and method
The solver uses an iterative method (Newton's method) that improves the guess step by step: xₙ₊₁ = xₙ − f(xₙ) ÷ f'(xₙ), until the change is smaller than the tolerance.
Worked example
For Math.pow(x, 2) - 10 with a guess of 3, the root found is about 3.1623, the square root of 10.
Tips
- Different starting guesses can find different roots.
- Use Math.pow(x, n), Math.sin(x), Math.log(x) and so on for functions.
Frequently Asked Questions
The method may need a better starting guess, or the equation may have no real root.