Math Calculator with Steps

by
Math Calculator with Steps
Quadratic Equation Solver (ax² + bx + c = 0)
Solution:
Enter coefficients to see the step-by-step solution.
function calculateMath(){var a=parseFloat(document.getElementById('coeff_a').value);var b=parseFloat(document.getElementById('coeff_b').value);var c=parseFloat(document.getElementById('coeff_c').value);var showSteps=document.getElementById('showSteps').checked;var ansDiv=document.getElementById('answer');if(isNaN(a)||isNaN(b)||isNaN(c)){ansDiv.innerHTML='Please enter valid numeric coefficients for a, b, and c.';return;}if(a==0){ansDiv.innerHTML='Coefficient "a" cannot be zero for a quadratic equation.';return;}var discriminant=(b*b)-(4*a*c);var stepsHTML=";if(showSteps){stepsHTML+='
';stepsHTML+='Step 1: Identify coefficients
a = '+a+', b = '+b+', c = '+c+'

';stepsHTML+='Step 2: Calculate the Discriminant (D)
Formula: D = b² – 4ac
';stepsHTML+='D = ('+b+')² – 4('+a+')('+c+')
';stepsHTML+='D = '+(b*b)+' – '+(4*a*c)+'
';stepsHTML+='D = '+discriminant+'

';}if(discriminant>0){var x1=(-b+Math.sqrt(discriminant))/(2*a);var x2=(-b-Math.sqrt(discriminant))/(2*a);if(showSteps){stepsHTML+='Step 3: Solve for x using Quadratic Formula
x = [-b ± √D] / 2a
';stepsHTML+='x = [-('+b+') ± √'+discriminant+'] / 2('+a+')
';stepsHTML+='x1 = ('+(-b)+' + '+Math.sqrt(discriminant).toFixed(4)+') / '+(2*a)+'
';stepsHTML+='x2 = ('+(-b)+' – '+Math.sqrt(discriminant).toFixed(4)+') / '+(2*a)+'
';}ansDiv.innerHTML=stepsHTML+'
Result:
x₁ = '+x1.toFixed(4)+'
x₂ = '+x2.toFixed(4)+'
';}else if(discriminant==0){var x=-b/(2*a);if(showSteps){stepsHTML+='Step 3: Solve for x (One Real Root)
x = -b / 2a
';stepsHTML+='x = -('+b+') / 2('+a+')
';}ansDiv.innerHTML=stepsHTML+'
Result:
x = '+x.toFixed(4)+'
';}else{var realPart=(-b/(2*a)).toFixed(4);var imagPart=(Math.sqrt(-discriminant)/(2*a)).toFixed(4);if(showSteps){stepsHTML+='Step 3: Complex Roots Detected
Since D < 0, the roots are imaginary.
x = [-b ± i√|D|] / 2a
';}ansDiv.innerHTML=stepsHTML+'
Result:
x₁ = '+realPart+' + '+imagPart+'i
x₂ = '+realPart+' – '+imagPart+'i
';}}

Calculator Use

This math calculator with steps is designed to solve quadratic equations in the form of ax² + bx + c = 0. Unlike standard calculators that only provide the final answer, this tool breaks down the mathematical process into logical segments, helping students and educators understand the underlying algebra.

To use the calculator, simply enter the numerical values for the coefficients (a, b, and c) and click "Calculate". The tool will immediately generate the discriminant and the roots of the equation.

Coefficient (a)
The number preceding the x-squared term. This cannot be zero.
Coefficient (b)
The number preceding the x term.
Constant (c)
The fixed number at the end of the equation.

How It Works

When you utilize our math calculator with steps, it follows the standard Quadratic Formula approach. The process is divided into calculating the discriminant and then applying the root formula.

Quadratic Formula: x = [-b ± √(b² – 4ac)] / 2a

  • The Discriminant (D): D = b² – 4ac. This determines the nature of the roots.
  • Two Real Roots: If D > 0, the equation has two distinct real solutions.
  • One Real Root: If D = 0, the equation has exactly one real solution (a repeated root).
  • Complex Roots: If D < 0, the solutions involve imaginary numbers (i).

Calculation Example

Example: Solve the equation x² – 5x + 6 = 0.

Step-by-step solution:

  1. Identify coefficients: a = 1, b = -5, c = 6
  2. Calculate Discriminant: D = (-5)² – 4(1)(6) = 25 – 24 = 1
  3. Since D > 0, solve for roots: x = [-(-5) ± √1] / 2(1)
  4. x1 = (5 + 1) / 2 = 3
  5. x2 = (5 – 1) / 2 = 2
  6. Result: x = 3, x = 2

Common Questions

Why do I need to see the steps?

Seeing the steps is crucial for learning. It helps verify where a mistake might have been made in manual calculations, such as signs (+/-) or basic arithmetic errors in the discriminant phase.

What happens if "a" is zero?

If a = 0, the equation is no longer quadratic; it becomes a linear equation (bx + c = 0). A quadratic equation must have a non-zero squared term.

Can this calculator handle negative numbers?

Yes, the math calculator with steps fully supports negative coefficients. Ensure you include the negative sign (e.g., -5) in the input fields for accurate results.

Leave a Comment