Rechner für wissenschaftliche Schreibweise

Gleichungsrechner

Lösen Sie lineare, quadratische und einvariable Gleichungen mit Schritten, Diskriminante, Residuum und Einsetzprobe.

GleichungMethodeLösung

Gleichungsrechner

Lösen Sie lineare, quadratische und einvariable Gleichungen mit Schritten, Diskriminante, Residuum und Einsetzprobe.

Bereit

Lösen Sie lineare, quadratische und einvariable Gleichungen mit Schritten, Diskriminante, Residuum und Einsetzprobe.

Schritt für Schritt

    Ergebnis

    Lösungen
    x = 4
    Gleichung
    2x + 3 = 11

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    Wandeln Sie wissenschaftliche Notation, Dezimalschreibweise, technische Notation und E-Notation klar formatiert um.

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    Gleichungsrechner

    Lösen Sie lineare, quadratische und einvariable Gleichungen mit Schritten, Diskriminante, Residuum und Einsetzprobe.

    What is an equation?

    An equation states that two mathematical expressions have the same value. Solving means finding every variable value that keeps the equality true. In 2x + 5 = 11, subtract 5 from both sides to get 2x = 6, then divide by 2, so x = 3. For x^2 - 5x + 6 = 0, factoring or the quadratic formula gives x = 2 or x = 3.

    How do you use the equation solver?

    Enter exactly one equals sign and choose the variable, usually x. The input can contain arithmetic, parentheses, powers, roots, logarithms and trigonometric functions. For exact algebraic answers, linear and quadratic equations are recognized first; broader expressions are scanned over the selected interval.

    After solving, read the method label. Linear exact solve means inverse operations isolated the variable. Quadratic exact solve means the discriminant was checked. Numerical root search means sign changes were located in the interval. The residual tells how close the computed root makes left minus right equal zero.

    Which equation examples should you check?

    Required examples: 2x + 5 = 11 gives x = 3. The quadratic x^2 - 5x + 6 = 0 gives x = 2 or x = 3. A fraction equation such as x/2 + 1 = 4 clears denominators first, giving x + 2 = 8 and x = 6.

    What equation mistakes should you avoid?

    Common mistakes include changing only one side of an equation, distributing parentheses incorrectly, losing a negative sign, dividing by zero, using too narrow a numerical search interval and forgetting to verify by substitution. Always apply the same operation to both sides and check the result in the original equation.

    Equation Solving Rules and Reference Tables

    These tables show the common algebra moves behind the solver. Each rule keeps the equality balanced: whatever is added, subtracted, multiplied or divided on one side must be applied to the other side as well.

    Addition and subtraction equations

    For one-step additive equations, undo addition with subtraction and undo subtraction with addition. This isolates the variable without changing equality.

    EquationInverse operationStep resultSolution
    x + 7 = 12Subtract 7 from both sidesx = 12 - 7x = 5
    x - 4 = 9Add 4 to both sidesx = 9 + 4x = 13

    Multiplication and division equations

    For multiplicative equations, divide by the coefficient or multiply by the denominator. The divisor must be nonzero.

    EquationInverse operationStep resultSolution
    4x = 28Divide both sides by 4x = 28 / 4x = 7
    x/3 = 5Multiply both sides by 3x = 5 x 3x = 15

    Two-step equations

    Two-step equations usually remove the constant first, then divide by the coefficient of the variable.

    EquationStep 1Step 2Solution
    3x + 5 = 20Subtract 5: 3x = 15Divide by 3x = 5
    2x - 7 = 9Add 7: 2x = 16Divide by 2x = 8

    Variable on both sides

    When the variable appears on both sides, collect variable terms on one side and constants on the other before dividing.

    EquationCollect variablesCollect constantsSolution
    5x = 3x + 145x - 3x = 14Divide by 2x = 7
    6x - 2 = 4x + 82x = 10Divide by 2x = 5

    Equations with parentheses

    Parentheses are handled with the distributive property before collecting like terms.

    EquationDistributeCollect termsSolution
    2(x + 3) = 102x + 6 = 102x = 4x = 2
    3(2x - 1) = 156x - 3 = 156x = 18x = 3

    Equations with fractions

    Fractions are cleared by multiplying every term by the least common denominator, then solving the simpler equation.

    EquationDenominatorCleared equationSolution
    x/2 + 1 = 4LCD = 2x + 2 = 8x = 6
    x/3 - x/6 = 2LCD = 62x - x = 12x = 12

    Checking solutions

    Substitution checks whether each proposed answer makes the original left side equal the original right side.

    EquationSimplifiedCandidateCheck
    2x + 5 = 112x = 6x = 32(3) + 5 = 11
    x^2 - 5x + 6 = 0x = 2, 3two roots0 = 0

    Ablauf

    Rechenablauf

    Enter equation
    Choose variable
    Solve
    Verify

    The solver parses both sides, moves terms into a single function, tries exact linear or quadratic solving, then uses numerical search when needed.

    Eingabeformate

    Unterstützte Formate

    Input typeExample
    Linear2x + 5 = 11
    Quadraticx^2 - 5x + 6 = 0
    Fractionx/2 + 1 = 4
    Functionsin(x) = 0.5

    Referenz

    Häufige wissenschaftliche Konstanten

    Zurück zum Rechner
    ConceptMeaningExampleUse
    Variableunknown valuexsolve target
    Rootsolution valuex = 3answer
    Residualleft minus right0verification

    Fragen

    Fragen zum Rechner

    How do you solve linear equations?

    Use inverse operations to isolate the variable. Add or subtract constants first, then divide by the variable coefficient. Apply every operation to both sides.

    How does the quadratic formula calculator step work?

    The solver identifies a quadratic form, calculates b^2 - 4ac, then uses the quadratic formula when real roots exist.

    Can it solve a system of equations?

    This page focuses on one-variable equations. A two-variable system needs a dedicated system solver or algebraic substitution outside this calculator.

    How do you solve for x?

    Move all x terms to one side, constants to the other side, then divide by the coefficient of x. Substitute the answer back to verify.

    What does the discriminant show?

    The discriminant b^2 - 4ac shows whether a quadratic has two real roots, one repeated real root, or no real roots.

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