M4.9.4 For the adult
Completing the square
I know (x + 3)² = x² + 6x + 9. How can I use a square to write x² + 6x + 2?
What this chapter teaches
Completing the square writes x² + bx + c as a square plus a number: half of b goes in the bracket, and its square is taken away. Then x appears once and a square root solves the equation, with both a positive and a negative root.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why do you add the square of half the x number, and why must you then take it away?
- How many solutions does (x + 3)² = 16 have, and what are they?
- What does the form (x + 3)² − 7 tell you about the smallest value of the expression?
After the chapter, the learner can
- Write x² + 6x + 2 as (x + 3)² − 7
- Solve a quadratic by completing the square
What they copy into their notebook
Half the x number goes in the bracket. Take away its square. Then add, take the square root, and use plus and minus.