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Math AI Solver Calculator

Equation Solver — Find x works out Result and Full-precision result from Expression, Angle unit and Significant figures. The default figures on this page give solution x of 1.414214; change any entry and the result, the working and the sources update together.

Solution x
1.414214
Scientific Calculator
Result
1.414214
Full-precision result
1.414214
Result with separators
1.414214
Scientific notation
1.414213562 x 10^0
Expression as parsed
x^2 - 2
Angle unit
rad
Result read as an angle, in degrees
81.028468
Result read as an angle, in radians
1.414214
f(x) - target at the solution
-0
Worked out from NIST Digital Library of Mathematical Functions, Chapter 4 (Elementary Functions) and 4 other sources.

Your figures

Updates as you type
Functions: abs, acos, acosh, asin, asinh, atan, atan2, atanh, cbrt, ceil, cos, cosh, cot, csc, deg, exp, fact, factorial, floor, gcd, hypot, lcm, ln, log, log10, log2, max, mean, min, mod, ncr, npr, pct, pow, rad, rem, root, round, sec, sign, sin, sinh, sqrt, sum, tan, tanh, trunc. Constants: e, phi, pi, tau. Also ! for factorial, ^ for powers, |x| for absolute value.
Applies to sin/cos/tan and their inverses. The CAS mode always works in radians, because the differentiation rules are only valid there.
Applied to the displayed result; the unrounded value is also returned.
Solver mode: the value the expression must take.
Graphing mode: the left edge of the window. Solver mode: the left end of the bracket to search.
Graphing mode: the right edge of the window. Solver mode: the right end of the bracket to search.
Graphing mode: how many evenly spaced x values to sample, endpoints included.

How this is worked out

5 steps
  1. Read as: x^2 - 2 with angles in radians.
  2. Solve f(x) = 0 on the bracket [0, 2].
  3. f(0) - 0 = -2 and f(2) - 0 = 2: the signs differ, so a solution lies between them.
  4. Bisecting the bracket to a width below 1e-13 gives x = 1.41421356237.
  5. Check: f(1.41421356237) - 0 = -1.28563826252e-13.
Step-by-step workingtable
Solve f(x) = 0 on the bracket [0, 2]., f(0) - 0 = -2 and f(2) - 0 = 2: the signs differ, so a solution lies between them., Bisecting the bracket to a width below 1e-13 gives x = 1.41421356237., Check: f(1.41421356237) - 0 = -1.28563826252e-13.

Its 9 worked examples are re-run on every release, last on 15 September 2026. What changed

Sources and references

5 sources
ECMA-262, ECMAScript Language Specification, §21.3 The Math Object
Defines the IEEE-754 double-precision behaviour of the elementary functions used here.
Burden & Faires, Numerical Analysis, §2.1 The Bisection Method
9th edition · The bracketing root-finder used by the solver mode.
Stewart, Calculus: Early Transcendentals, Chapter 3 (Differentiation Rules)
8th edition · The product, quotient, chain and power rules implemented in core/symbolic.ts and used by the CAS mode.

What the Equation Solver — Find x calculates

Evaluates a scientific expression with trigonometric, inverse and hyperbolic functions, logarithms to any base, roots, powers, factorials and combinatorics, honouring standard operator precedence and an explicit angle unit; also tabulates y = f(x) for graphing, solves f(x) = target for x by bisection, and simplifies and differentiates an expression symbolically.

How to use this Equation Solver — Find x

Enter Expression, Angle unit, Significant figures and Solve for f(x) =. Result updates as you type. Change one figure at a time to see what drives the result.

How the result is worked out

Open “How this is worked out” beside the result for the step-by-step calculation behind Result, Full-precision result and Result with separators.

The method follows NIST Digital Library of Mathematical Functions, Chapter 4 (Elementary Functions), Abramowitz & Stegun, Handbook of Mathematical Functions, Chapter 4, ECMA-262, ECMAScript Language Specification, §21.3 The Math Object, Burden & Faires, Numerical Analysis, §2.1 The Bisection Method and Stewart, Calculus: Early Transcendentals, Chapter 3 (Differentiation Rules).

What you can compare

Change one input at a time to see how it affects Result, Full-precision result and Result with separators. The inputs you can vary are Expression, Angle unit, Significant figures, Solve for f(x) =, Window / bracket: smallest x and Window / bracket: largest x.

Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.

Embed this calculator on your website

Copy this code into any page. The calculator appears with the figures currently entered, sizes itself to fit, and a small credit line links back here. Free, no account, no ads inside it, no tracking of your readers. Set your own figures and fixed fields; Personal removes the credit line, sets your colour and shows you which sites use it.

Preview

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Frequently asked questions

Is there a free AI math solver available?

The calculation is free and does not require an account. An account is only needed for optional features such as saving, comparing, exporting, or sharing supported scenarios.

Which AI math solver is the most accurate?

The Equation Solver — Find x follows the stated method, but the result is only as reliable as Expression, Angle unit, Significant figures, Solve for f(x) = and Window / bracket: smallest x and the assumptions shown. Check the working and sources before relying on it for an important decision.

Can Chatgpt solve math?

Evaluates a scientific expression with trigonometric, inverse and hyperbolic functions, logarithms to any base, roots, powers, factorials and combinatorics. On the figures this page opens with — solve for f(x) = 10, window / bracket: smallest x 0 and window / bracket: largest x 10 — the solution x is 1.414214. Put your own figures in their place and the working updates beside the result.

What information do I need for the Equation Solver — Find x?

You need Expression, Angle unit, Significant figures, Solve for f(x) =, Window / bracket: smallest x, Window / bracket: largest x and Points to tabulate. The page opens with default figures that give solution x of 1.414214, so you can see the scale before entering your own.

What does this Equation Solver — Find x show?

It shows Result, Full-precision result, Result with separators, Scientific notation, Expression as parsed, Angle unit, Result read as an angle, in degrees and Result read as an angle, in radians, with the working and any warnings for your entries.

Can I check how the Equation Solver — Find x result was calculated?

Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.

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