Algebra Calculator

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Algebra Calculator
Linear Equation: ax + b = cQuadratic Equation: ax² + bx + c = 0Slope-Intercept: y = mx + b (Solve for y)
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Solution:

Result =

function updateLabels(){var type=document.getElementById('calc_type').value;var l1=document.getElementById('label1');var l2=document.getElementById('label2');var l3=document.getElementById('label3');var i3=document.getElementById('input3′);if(type==='linear'){l1.innerHTML='Coefficient (a):';l2.innerHTML='Coefficient (b):';l3.innerHTML='Constant (c):';i3.parentElement.parentElement.style.display='table-row';}else if(type==='quadratic'){l1.innerHTML='Coefficient (a):';l2.innerHTML='Coefficient (b):';l3.innerHTML='Constant (c):';i3.parentElement.parentElement.style.display='table-row';}else if(type==='slope'){l1.innerHTML='Slope (m):';l2.innerHTML='Input (x):';l3.innerHTML='Y-Intercept (b):';i3.parentElement.parentElement.style.display='table-row';}}function calculateAlgebra(){var type=document.getElementById('calc_type').value;var a=parseFloat(document.getElementById('input1').value);var b=parseFloat(document.getElementById('input2').value);var c=parseFloat(document.getElementById('input3').value);var display=document.getElementById('answer');var showSteps=document.getElementById('showSteps').checked;var resultHtml=";if(isNaN(a)||isNaN(b)||isNaN(c)){alert('Please enter valid numerical coefficients.');return;}if(type==='linear'){if(a===0){resultHtml='No solution (a cannot be 0)';}else{var x=(c-b)/a;resultHtml='x = '+x.toFixed(4)+'';if(showSteps){resultHtml+='
Steps:
1. Subtract '+b+' from both sides: '+a+'x = '+(c-b)+'
2. Divide by '+a+': x = '+(c-b)+'/'+a+'
';}}}else if(type==='quadratic'){var disc=(b*b)-(4*a*c);if(a===0){resultHtml='This is not a quadratic equation (a=0).';}else if(disc<0){resultHtml='No Real Roots (Complex roots exist)';}else if(disc===0){var x=(-b)/(2*a);resultHtml='x = '+x.toFixed(4)+'';}else{var x1=((-b)+Math.sqrt(disc))/(2*a);var x2=((-b)-Math.sqrt(disc))/(2*a);resultHtml='x₁ = '+x1.toFixed(4)+'
x₂ = '+x2.toFixed(4)+'';}if(showSteps&&a!==0){resultHtml+='
Steps:
1. Discriminant (D) = b² – 4ac = '+(b*b)+' – '+(4*a*c)+' = '+disc+'
2. Use formula: x = [-b ± √D] / 2a
';}}else if(type==='slope'){var y=(a*b)+c;resultHtml='y = '+y.toFixed(4)+'';if(showSteps){resultHtml+='
Steps:
1. Equation: y = ('+a+')( '+b+' ) + '+c+'
2. y = '+(a*b)+' + '+c+'
';}}display.innerHTML=resultHtml;}updateLabels();

Algebra Calculator Use

This algebra calculator is designed to help students, educators, and professionals solve complex algebraic equations quickly. Whether you are working with basic linear relationships or solving for roots in a quadratic function, this tool provides precise answers and step-by-step logic.

To use the calculator, simply select the equation type that matches your problem, enter the coefficients, and click "Solve." Our tool handles various forms including the quadratic formula, linear equality, and slope-intercept form.

Coefficient (a)
The number multiplying the highest degree variable (e.g., the 'a' in ax²).
Coefficient (b)
The number multiplying the secondary variable (e.g., the 'b' in bx).
Constant (c)
The fixed numerical value in the equation that does not have a variable attached.

How It Works

The algebra calculator uses standard mathematical algorithms to process your inputs. For quadratic equations, it utilizes the famous Quadratic Formula to identify where a parabola crosses the x-axis.

x = [-b ± √(b² – 4ac)] / 2a

  • Discriminant (b² – 4ac): Determines the nature of the roots. If positive, there are two real roots. If zero, one real root. If negative, the roots are imaginary.
  • Linearity: For linear equations (ax + b = c), the calculator isolates x by performing inverse operations.
  • Slope-Intercept: Calculates the value of 'y' given the slope (m), the x-value, and the y-intercept (b).

Calculation Example

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

Step-by-step solution:

  1. Identify coefficients: a = 1, b = -5, c = 6
  2. Calculate discriminant: (-5)² – 4(1)(6) = 25 – 24 = 1
  3. Apply formula: x = [5 ± √1] / 2
  4. x₁ = (5 + 1) / 2 = 3
  5. x₂ = (5 – 1) / 2 = 2
  6. Result: x = 3, 2

Common Questions

What is an algebra calculator?

An algebra calculator is a digital tool that solves mathematical equations by performing algebraic operations. It helps find the value of unknown variables by following order of operations and algebraic rules.

Can this calculator solve for imaginary numbers?

Currently, this calculator focuses on "Real Roots." If the discriminant is negative, it will notify you that the roots are complex (imaginary), which is essential for understanding the limits of real-number algebra.

Why is the 'a' coefficient important in quadratics?

The 'a' coefficient determines the direction and width of the parabola. If 'a' is positive, it opens upward; if negative, it opens downward. If 'a' is zero, the equation is no longer quadratic but becomes a linear equation.

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