Completing the Square with Radical Answers | Solve x² – 10x + 18 = 0 | SciRender | English
Learn how to solve x² – 10x + 18 = 0 by completing the square – and leave your answer in simplest radical form.
This tutorial carefully handles the negative coefficient and shows why the final answer is x = 5 ± √7.
📐 What you’ll learn:
1. Move the constant: x² – 10x = –18
2. Take half of –10 (–5) and square it → +25
3. Add 25 to both sides: x² – 10x + 25 = 7
4. Factor as (x – 5)² = 7
5. Square root both sides: x – 5 = ±√7
6. Solve: x = 5 ± √7
🧠 Geometric insight: See x² – 10x as an incomplete square missing a 5×5 corner, completed by adding 25 – making the perfect square (x – 5)².
✏️ Perfect for students who need to express answers in simplest radical form and understand the “why” behind the method.
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