How to Solve Quadratic Equations
A quadratic equation has degree 2. Write it as ax² + bx + c = 0, then factor, complete the square, or use the quadratic formula.
What is a quadratic equation?
A quadratic equation is an equation in which the highest power of the variable is 2. Its standard form is ax² + bx + c = 0.
Step-by-step method
- Write ax² + bx + c = 0.
- Compute Δ = b² − 4ac.
- If you cannot factor quickly, use x = (−b ± √Δ) / (2a).
- Substitute each root to verify.
Example
x² − 5x + 6 = 0
- Δ = 25 − 24 = 1
- x = (5 ± 1)/2
- x = 3 or x = 2
Answer: x = 2, x = 3
Interactive example
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Example problems
Common mistakes
b has the wrong sign
In x² − 5x + 6 = 0, b = −5.
Forgetting two solutions
Unless Δ = 0, report both roots.
Related formulas
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Related guides
Frequently asked questions
When is the discriminant negative?
There are no real solutions. The roots are complex conjugates.