How it finds the answers
Whatever you type is rearranged to f(x) = 0 — 3x + 1 = x + 7 becomes 2x − 6 = 0. The solver then walks across the search range looking for places where f changes sign, because a continuous function that goes from negative to positive must cross zero somewhere in between. Each crossing is then narrowed by bisection until it is pinned to full precision.
That approach has a real advantage over the quadratic formula: it works on anything you can write down. sin(x) = 0.5, e^x = 5 and x^5 − 3x = 1 are all the same problem to it.
Why there is a search range
A numeric solver has to look somewhere. The default −50 to 50 covers most textbook problems, but sin(x) = 0 has infinitely many solutions and the range decides how many you see. If an answer you expect is missing, widen the range.
The residual shown under the results is how far from zero the equation actually is at each answer. It is the honest check on a numeric method — a residual of 1e-12 means the root is real, not a rounding artefact.
What it will miss
A root the function touches without crossing — like x² − 2x + 1 = 0 at x = 1 — has no sign change, so it is found only because the scan happens to land close to zero. Complex solutions are not found at all; for those, use the quadratic formula calculator, which reports them exactly.
Frequently asked questions
Can it solve for two unknowns?
No — a single equation with two unknowns has infinitely many solutions. For a system of simultaneous equations, use the matrix calculator's solve function.
Is anything uploaded?
No. The equation is solved in the page and never transmitted.
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