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Common Use Cases
- Algebra homework — check solutions and understand each step
- Physics problems — solve for unknown variables in formulas
- Engineering calculations — find roots of characteristic equations
- Financial math — solve for interest rates, time periods, or payment amounts
- Optimization — find where a function equals zero (break-even analysis)
The Equation Solver on TechConverter.me shows every algebraic step clearly, making it both a problem-solving tool and a learning resource for anyone working with mathematical equations.
Examples
Example 1: Linear Equation
Solving: 3x + 7 = 22
Step 1: Subtract 7 from both sides
3x + 7 - 7 = 22 - 7
3x = 15
Step 2: Divide both sides by 3
3x / 3 = 15 / 3
x = 5
Solution: x = 5
Verification: 3(5) + 7 = 15 + 7 = 22 ✓
Example 2: Quadratic Equation
Solving: 2x² - 5x - 3 = 0
Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
a = 2, b = -5, c = -3
Step 1: Calculate the discriminant
Δ = b² - 4ac = (-5)² - 4(2)(-3) = 25 + 24 = 49
Δ > 0 → two distinct real solutions
Step 2: Apply the quadratic formula
x = (5 ± √49) / (2 × 2)
x = (5 ± 7) / 4
Step 3: Calculate both solutions
x₁ = (5 + 7) / 4 = 12 / 4 = 3
x₂ = (5 - 7) / 4 = -2 / 4 = -1/2
Solutions: x = 3 or x = -0.5
Factored form: 2(x - 3)(x + 1/2) = 0
Example 3: Quadratic with Complex Solutions
Solving: x² + 4x + 13 = 0
Discriminant: Δ = 4² - 4(1)(13) = 16 - 52 = -36
Δ < 0 → two complex (non-real) solutions
x = (-4 ± √(-36)) / 2
x = (-4 ± 6i) / 2
Solutions: x = -2 + 3i and x = -2 - 3i