One-step isolation
Solve 3x-7=11
Method: Use inverse operations.
- 1Add 7 to both sides to get 3x=18.
- 2Divide both sides by 3.
- 3Check that 3(6)-7 equals 11.
Final answer
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Equation Solver
Solve linear, quadratic, polynomial, and systems of equations with step-by-step explanations and verification.
Step-by-step solutions
Clear, detailed explanations
Instant results
Accurate answers in seconds
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How to Use the Equation Solver
1
Enter the equation
Type an equation or system of equations.
2
Identify the strategy
We choose factoring, quadratic formula, substitution, or elimination.
3
Verify solutions
Each solution is checked against the original equation.
Example
How the Equation Solver Chooses a Method
Solve for an unknown and verify which candidate values satisfy the original equation.
The solver classifies the equation by degree and structure, applies reversible operations or a suitable polynomial method, and checks candidate roots in the original input to catch extraneous solutions.
Supported problem types
- Linear and quadratic equations
- Common polynomial and rational equations
- Single-variable equations with exact or numerical roots
Limits and assumptions
- Squaring or clearing denominators can introduce candidates that must be rejected.
- Some transcendental equations require numerical approximations.
Worked Equation Solver Examples
Each example names the method, shows the ordered reasoning, and keeps the final answer separate so you can check your own work.
Quadratic roots
Solve x^2-5x+6=0
Method: Factor the quadratic.
- 1Find two numbers with product 6 and sum -5.
- 2Write (x-2)(x-3)=0.
- 3Apply the zero-product property.
Final answer
Rational restriction
Solve (x+1)/(x-2)=2
Method: Record the denominator restriction before clearing it.
- 1Require x not equal to 2.
- 2Multiply by x-2 to get x+1=2x-4.
- 3Solve x=5 and verify it is allowed.
Final answer
Learn This Topic
What the Equation Solver Helps You Understand
Solve linear, quadratic, polynomial, and systems of equations with step-by-step explanations and verification.
Learning focus 1
Type an equation or system of equations.
Learning focus 2
We choose factoring, quadratic formula, substitution, or elimination.
Learning focus 3
Each solution is checked against the original equation.
Input tips
- • Type an equation or system of equations.
- • Yes. Enter multiple equations separated by 'and' to solve systems.
Common mistakes to avoid
- • Dividing by an expression that may be zero.
- • Keeping extraneous roots introduced by squaring or clearing denominators.
Frequently Asked Questions
Can this solve systems of equations?
Yes. Enter multiple equations separated by 'and' to solve systems.
Does it show the quadratic formula?
When applicable, the solver shows the quadratic formula and substitution steps.
Why can an equation have an extraneous solution?
Non-reversible operations such as squaring can create candidates, so they must be checked in the original equation.
Can the result be an approximation?
Yes. Equations without a convenient symbolic form may be solved numerically and clearly marked as approximate.
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