Math Solver Calculator

Solve linear equations, quadratic equations, and systems of two equations with step-by-step explanations.

ax + b = c

Solution for x

5

From 3x + 7 = 22

Equation type

Linear

First-degree equation with one unknown variable.

Verification

22

3(5) + 7 should equal 22

Step-by-step solution

  1. Start: 3x + 7 = 22
  2. Subtract 7: 3x = 15
  3. Divide by 3: x = 5

How it works

A math solver calculator is useful because algebra is the part of math where most people get stuck. The mechanics of isolating a variable, applying the quadratic formula, or solving simultaneous equations are straightforward in theory but easy to mess up in practice. A solver that shows step-by-step workings is more valuable than one that just prints an answer, because users can verify where they went wrong and learn the process.

This solver handles three equation types. Linear equations of the form ax + b = c are solved by isolating x through subtraction and division. Quadratic equations use the quadratic formula with discriminant analysis to determine whether roots are real, repeated, or complex. Systems of two linear equations are solved with Cramer's rule using 2×2 determinants. Each mode displays intermediate steps so users can follow the logic and catch errors in their own work.

Frequently asked questions

What types of equations can this solve?

Linear equations of the form ax + b = c, quadratic equations of the form ax² + bx + c = 0, and systems of two linear equations with two unknowns.

What is the discriminant in a quadratic equation?

The discriminant is b² − 4ac. It determines the nature of the roots: positive means two real roots, zero means one repeated root, and negative means two complex roots.

How does the system solver work?

It uses Cramer's rule, which relies on determinants to find the unique intersection point of two lines. If the determinant is zero, the lines are parallel or identical.

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