Equations and systems — type it like in a textbook, get a step-by-step solution
Equation
System of linear equations
📚 Theory: how to solve equations
A linear equation ax + b = 0 is solved by moving terms: x-terms to the left, numbers to the right (the sign flips when moving), then divide both sides by the coefficient of x.
A quadratic equation ax² + bx + c = 0 is solved via the discriminant D = b² − 4ac. If D > 0 — two roots, D = 0 — one root, D < 0 — no real roots. Roots: x = (−b ± √D) / 2a.
A cubic equation ax³ + bx² + cx + d = 0 is solved at school by guessing: if there is a “nice” (rational) root, it must be among ±p/q, where p divides the constant term and q divides the leading coefficient. Once a root is found, divide the polynomial by (x − root) — a plain quadratic remains.
A system of linear equations is solved by Gaussian elimination: add equations to each other to eliminate unknowns one by one until the last equation has only one — then substitute the found values from the bottom up (back substitution).
Free-form input: 2x+6=0, 3(x-1)=2x+5, y*9, fractions and decimals are fine. In the system each line is one equation, variables are any letters (x, y, z…).
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