Math Calculator with Steps

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Math Calculator with Steps (Quadratic Solver)
Quadratic Equation (ax² + bx + c = 0)
function calculateMathSteps(){var a=parseFloat(document.getElementById('input_a').value);var b=parseFloat(document.getElementById('input_b').value);var c=parseFloat(document.getElementById('input_c').value);var showSteps=document.getElementById('showSteps').checked;var answerDiv=document.getElementById('calculatorAnswer');var content=document.getElementById('answerContent');if(isNaN(a)||isNaN(b)||isNaN(c)){alert('Please enter valid numeric values for all coefficients.');return;}if(a==0){content.innerHTML='Result: Not a quadratic equation (a cannot be 0). This is a linear equation: '+b+'x + '+c+' = 0. Solving for x: x = '+(-c/b).toFixed(4);answerDiv.style.display='block';return;}var disc=(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 = b² – 4ac)
';stepsHtml+='D = ('+b+')² – 4('+a+')('+c+')
';stepsHtml+='D = '+(b*b)+' – '+(4*a*c)+'
';stepsHtml+='D = '+disc+'

';}if(disc>0){var x1=(-b+Math.sqrt(disc))/(2*a);var x2=(-b-Math.sqrt(disc))/(2*a);if(showSteps){stepsHtml+='Step 3: Apply the Quadratic Formula
';stepsHtml+='x = [-b ± √D] / 2a
';stepsHtml+='x = [-('+b+') ± √'+disc+'] / 2('+a+')
';stepsHtml+='x = ['+(-b)+' ± '+Math.sqrt(disc).toFixed(4)+'] / '+(2*a)+'

';stepsHtml+='Step 4: Solve for both roots
';stepsHtml+='x₁ = '+(-b+Math.sqrt(disc)).toFixed(4)+' / '+(2*a)+' = '+x1.toFixed(4)+'
';stepsHtml+='x₂ = '+(-b-Math.sqrt(disc)).toFixed(4)+' / '+(2*a)+' = '+x2.toFixed(4)+'
';}content.innerHTML='
Two Real Roots Found:
'+stepsHtml+'
x₁ = '+x1.toFixed(4)+'
x₂ = '+x2.toFixed(4)+'
';}else if(disc==0){var x=-b/(2*a);if(showSteps){stepsHtml+='Step 3: Solve for the single root (D=0)
';stepsHtml+='x = -b / 2a
';stepsHtml+='x = -('+b+') / 2('+a+')
';stepsHtml+='x = '+(-b)+' / '+(2*a)+'
';}content.innerHTML='
One Real Root Found:
'+stepsHtml+'
x = '+x.toFixed(4)+'
';}else{var realPart=(-b/(2*a)).toFixed(4);var imagPart=(Math.sqrt(-disc)/(2*a)).toFixed(4);if(showSteps){stepsHtml+='Step 3: Calculate Complex Roots (D < 0)
';stepsHtml+='x = [-b ± i√|D|] / 2a
';}content.innerHTML='
Complex Roots Found:
'+stepsHtml+'
x₁ = '+realPart+' + '+imagPart+'i
x₂ = '+realPart+' – '+imagPart+'i
';}if(showSteps){stepsHtml+='
';}answerDiv.style.display='block';}

Calculator Use

The math calculator with steps is an essential tool for students and professionals looking to solve quadratic equations efficiently. Unlike standard calculators that only provide the final answer, this tool breaks down the logic into manageable parts, allowing you to follow the math from start to finish. This is particularly useful for learning the quadratic formula and verifying homework assignments.

To use this calculator, simply enter the coefficients of your quadratic equation (ax² + bx + c = 0) into the input fields above. You can toggle the "Show Solution Steps" checkbox to view the discriminant calculation and the application of the quadratic formula.

Coefficient (a)
The number preceding the x² term. This cannot be zero for a quadratic equation.
Coefficient (b)
The number preceding the x term.
Coefficient (c)
The constant term (the number without a variable).

How It Works

The math calculator with steps utilizes the standard Quadratic Formula to find the roots (x-intercepts) of any given equation. The process involves identifying the relationship between the coefficients and the discriminant to determine if the roots are real or complex.

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

  • Discriminant (D): Calculated as b² – 4ac. If D > 0, there are two distinct real roots. If D = 0, there is exactly one real root. If D < 0, the roots are complex (imaginary).
  • Real Part: The portion of the solution calculated by -b / 2a.
  • Imaginary Part: Found when the discriminant is negative, represented using the unit 'i'.

Calculation Example

Example: Solve the equation x² – 5x + 6 = 0 using the math calculator with steps.

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, calculate two roots.
  4. x = [-(-5) ± √1] / 2(1)
  5. x = [5 ± 1] / 2
  6. x₁ = (5+1)/2 = 3; x₂ = (5-1)/2 = 2
  7. Final Answer: x = 3, x = 2.

Common Questions

What happens if 'a' is zero?

If the 'a' coefficient is zero, the equation is no longer quadratic; it becomes a linear equation (bx + c = 0). The quadratic formula cannot be applied because it involves division by 2a, which would result in division by zero.

Can this calculator handle negative numbers?

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

Why are the steps important?

Viewing the steps helps users identify where they might have made a manual error, such as forgetting to square a negative number correctly or mishandling the signs within the discriminant calculation.

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