Equation Solver
Solve common algebra equations step by step, including linear, quadratic, rational, absolute value, radical, exponential, and logarithmic equations.
Background
An equation says two expressions are equal. Solving an equation means finding the value or values of x that make both sides match. This solver focuses on student-friendly algebra patterns and shows the method, steps, checks, plain-English explanations, common mistakes, and graph insight.
How to use this equation solver
- Choose Auto Solve or select a specific equation type.
- Enter a one-variable equation using x.
- Use ^ for powers, such as x^2.
- Click Solve, or keep Auto-solve while typing turned on for instant feedback.
How this calculator works
- Linear equations are solved by collecting x-terms and constants.
- Quadratic equations are solved using the quadratic formula.
- Simple rational equations are solved by clearing constant denominators.
- Absolute value equations split into two possible cases.
- Radical equations isolate the square root, square both sides, and check for extraneous answers.
- Exponential equations use same-base recognition or logarithms.
- Logarithmic equations rewrite the log equation in exponential form.
Formula & Equations Used
Linear equation: ax + b = 0 → x = −b / a
Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a
Absolute value equation: |A| = k → A = k or A = −k
Radical equation: √A = k → A = k²
Exponential equation: a^x = b → x = log(b) / log(a)
Logarithmic equation: log_b(x) = y → x = b^y
Example Problems & Step-by-Step Solutions
Example 1 — Solve 2x + 5 = 17
- Subtract 5 from both sides: 2x = 12.
- Divide by 2: x = 6.
Example 2 — Solve x² − 5x + 6 = 0
- Identify a = 1, b = −5, and c = 6.
- Use the quadratic formula.
- The solutions are x = 2 and x = 3.
Example 3 — Solve |x − 4| = 7
- Split into two cases: x − 4 = 7 or x − 4 = −7.
- Solve each case.
- The solutions are x = 11 and x = −3.
Frequently Asked Questions
Q: What types of equations can this solver handle?
It supports common student-friendly one-variable equations, including linear, quadratic, simple rational, absolute value, radical, exponential, and logarithmic equations.
Q: Can this solver show steps?
Yes. It explains the method and gives step-by-step work for supported equation types.
Q: Does the calculator check answers?
Yes. When possible, it substitutes each solution back into the original equation.
Q: Why can radical equations create extraneous solutions?
Squaring both sides can introduce answers that do not work in the original equation, so radical equation solutions must be checked.
Q: Is this a full computer algebra system?
No. It is designed as an educational equation solver for common algebra patterns students see in class.
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