Math AI Solver Calculator

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.
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.

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.

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