Ray's New Elementary Algebra · Art. 213 · Unit 7: Chapter VII: Quadratic equations
47. The Hindoo method
Goal: Your student solves ax² + bx = c without fractions by multiplying by 4a and adding b².
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
- A card to cover printed answers
What's in the book
The Hindoo method of completing the square, explained, with its rule, one worked example (3x² − 5x = 28) and five exercises. Answers are printed.
The lesson, step by step
Warm-up
Solve x² − x = 42 by completing the square. (7 or −6; it needs quarters.)
The idea
Read Art. 213.
When an equation is brought to the form ax²+bx=c, it may be reduced to a simple equation, without dividing by the coefficient of x²; thus avoiding fractions.
The rule
1. Reduce the equation to the form ax²+bx=c, and multiply both sides by four times the coefficient of x².
2. Add the square of the coefficient of x to each side, and extract the square root.
Work the example together
3x² − 5x = 28. Multiply by 12: 36x² − 60x = 336. Add 25: 36x² − 60x + 25 = 361. Root: 6x − 5 = ±19. So x = 4 or −7/3.
Guided practice
Your student does exercise 2 (2x² + 5x = 33; 3 or −11/2) while you watch, then redoes the warm-up by this method.
Independent practice
Exercises 3 to 6. Compare with the printed answers.
Wrap-up
Ask: Which method do you prefer for 5x² + 2x = 88? Why?
Tip
A short lesson. If time remains, start on the problems in the next guide.
Answers to the book's problems
The book prints the answer after each exercise.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in the Key ↗.