How to solve quadratic equations step by step
Use this guide to review the main solution routes for quadratics before trying your own equation in CureMath — AI Math Explainer.
What this topic means and what to look for first.
A quadratic equation usually has the form ax^2 + bx + c = 0.
The best method depends on how easy the expression is to factor and whether you need an exact general route.
One reliable route through the topic.
- 1Rearrange the equation so one side is 0.
- 2Check whether the expression factorises cleanly.
- 3If it factorises, solve each bracket by setting it equal to 0.
- 4If it does not factorise easily, use the quadratic formula.
- 5Check both answers by substitution if the result matters.
See the method in action.
x^2 + 5x + 6 = 0
- Factorise to (x + 2)(x + 3) = 0.
- Set each bracket equal to 0.
- So x = -2 or x = -3.
2x^2 + 3x - 2 = 0
- Use a = 2, b = 3, c = -2.
- Substitute into the quadratic formula.
- The solutions are x = 0.5 and x = -2.
Things that commonly send the method off track.
- Forgetting to move everything to one side before solving.
- Dropping a negative sign when substituting into the formula.
- Stopping after finding only one root.
Want to test your own problem next?
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A free account is the current follow-up route for returning to the solver beta and future guide updates as the public library grows.
Want to try a similar problem yourself?
Create a free account if you want to use the solver beta after reading the guide.
A free account is the current follow-up route for returning to the solver beta and future guide updates as the public library grows.
Extra algebra revision resources
If you want more printed algebra practice after this page, these broader searches are a sensible next step.
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Algebra workbook and revision book search
Useful if you want more equation, factorising, and worked-example practice in one printed source.
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GCSE algebra practice resources search
A wider GCSE-style search if you want more mixed algebra questions beyond one online guide.
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Short answers worth checking.
Factorise first when the numbers are simple and the brackets are easy to spot.
Yes. If the quadratic has a repeated root, both solutions are the same value.
Continue with the next closely related topic.
Use the public site structure first, then switch into the solver tool only if you need a direct test.
CureMath uses artificial intelligence to suggest how a maths problem could potentially be solved. AI can make mistakes.
Check important answers independently before relying on them.