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Online Calculator with Variables and Square Roots

Reviewed by Calculator Editorial Team

This online calculator helps you solve equations with variables and square roots. Whether you're a student learning algebra or a professional needing quick calculations, this tool provides accurate results and step-by-step guidance.

How to use this calculator

Using our online calculator with variables and square roots is simple:

  1. Enter your equation in the input field. Use the format like "x² + 5x + 6 = 0" or "√x = 16".
  2. Select the type of equation you're solving (quadratic, square root, etc.).
  3. Click "Calculate" to see the solution.
  4. Review the detailed solution steps in the result panel.

The calculator will solve for the variable (usually x) and show all steps of the solution process.

Tip

For square root equations, make sure the number under the square root is non-negative. The calculator will alert you if the equation has no real solutions.

Formulas used

The calculator uses standard algebraic formulas to solve equations:

Quadratic Equation

For equations of the form ax² + bx + c = 0:

x = [-b ± √(b² - 4ac)] / (2a)

Square Root Equation

For equations of the form √x = k:

x = k²

These formulas are applied based on the type of equation you input.

Worked examples

Example 1: Quadratic Equation

Solve x² - 5x + 6 = 0

  1. Identify coefficients: a=1, b=-5, c=6
  2. Calculate discriminant: D = b² - 4ac = 25 - 24 = 1
  3. Apply quadratic formula: x = [5 ± √1]/2
  4. Solutions: x = (5+1)/2 = 3 and x = (5-1)/2 = 2

Example 2: Square Root Equation

Solve √x = 4

  1. Square both sides: x = 4² = 16
  2. Solution: x = 16

Frequently Asked Questions

What types of equations can this calculator solve?

This calculator can solve quadratic equations (ax² + bx + c = 0) and square root equations (√x = k). It can also handle equations with variables in other positions.

What if my equation has no real solutions?

For quadratic equations, if the discriminant (b² - 4ac) is negative, there are no real solutions. The calculator will notify you of this and show the complex solutions if needed.

Can I solve equations with more than one variable?

This calculator is designed for equations with one variable. For systems of equations with multiple variables, you would need a different tool.