Completing The Square Calculator
Free completing the square calculator — step-by-step solution, worked examples, instant answers.
Completing the square — rewrites ax² + bx + c in vertex form a(x + p)² + q.
About Completing The Square Calculator
The Completing The Square Calculator solves ax² + bx + c = a(x + b/2a)² + (c − b²/4a) for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. Completing the square is how the quadratic formula is derived, and it is still the fastest route to a parabola's vertex and extreme value.
How to use Completing The Square Calculator
- 1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
- 2The tool substitutes them into ax² + bx + c = a(x + b/2a)² + (c − b²/4a) and recomputes live.
- 3Read the answer in the result box, then expand the step-by-step solution to see the full working.
- 4Copy the method into your notebook, or change inputs to explore how the result behaves.
Why use Completing The Square Calculator?
- ✓Solves ax² + bx + c = a(x + b/2a)² + (c − b²/4a) instantly as you type — no submit button, no waiting
- ✓Step-by-step solution shown for every calculation, not just the final answer
- ✓Realistic example values pre-loaded so you can see a worked example immediately
- ✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
- ✓Mobile-friendly and fast enough to use mid-homework or mid-lesson
Frequently asked questions
What formula does the Completing The Square Calculator use?+
It uses ax² + bx + c = a(x + b/2a)² + (c − b²/4a). The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.
What should I keep in mind when using this calculator?+
Completing the square is how the quadratic formula is derived, and it is still the fastest route to a parabola's vertex and extreme value. The sign rule: the number inside the bracket is +b/2a, but the vertex x-coordinate is −b/2a.
Is the Completing The Square Calculator free to use?+
Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.
Can I use this for homework, teaching or exam prep?+
That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.
Embed Completing The Square Calculator on your website
Want Completing The Square Calculatoron your own site? Paste this snippet into any HTML page — it's free, with no API key or sign-up. The tool loads in an iframe and keeps working exactly as it does here.
<iframe src="https://tooljolt.com/tools/completing-the-square-calculator" width="100%" height="640" style="border:1px solid #e5e7eb;border-radius:12px;max-width:680px" title="Completing The Square Calculator — ToolJolt" loading="lazy"></iframe>Related Science tools
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