1. Completing the Square
Algebra Review

2. Solve 2+ 𝑥 2 =6𝑥 by completing the square
𝑥 2 −6𝑥=−2 𝑥 2 −6𝑥 + =−2 𝑥−3 2 =
Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐
Add 𝑏 to both sides
Factor & Simplify
Square root both sides
Solve for 𝑥

3. Solve 2+ 𝑥 2 =6𝑥 by completing the square
𝑥 2 −6𝑥=−2 𝑥 2 −6𝑥+9=−2 +9 𝑥−3 2 =7 𝑥−3=± 7 𝑥=3± 7
Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐
Add 𝑏 to both sides
Factor & Simplify
Square root both sides
Solve for 𝑥

4. Solve 𝑥 2 +5𝑥−24=0 by completing the square
𝑥 2 +5𝑥=24 𝑥 2 +5𝑥 + ? ? =24 + ? ? 𝑥 = ?
Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐
Add 𝑏 to both sides
Factor & Simplify
Square root both sides
Solve for 𝑥

5. Solve 𝑥 2 +5𝑥−24=0 by completing the square
𝑥 2 +5𝑥=24 𝑥 2 +5𝑥 = 𝑥 = 𝑥+ 5 2 =± 11 2 𝑥= 11 2 − 5 2 & − 11 2 − 5 2 𝑥=3 & −8
Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐
Add 𝑏 to both sides
Factor & Simplify
Square root both sides
Solve for 𝑥

6. Solve 5− 3 2 𝑥= 𝑥 2 by completing the square
5= 𝑥 𝑥 𝑥 𝑥+ ? ? =5+ ? ? 𝑥 = ?
Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐
Add 𝑏 to both sides
Factor & Simplify
Square root both sides
Solve for 𝑥

7. Solve 5− 3 2 𝑥= 𝑥 2 by completing the square
5= 𝑥 𝑥 𝑥 𝑥 = 𝑥 = 𝑥+ 3 4 =± 89 4 𝑥= −3± 89 4
Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐
Add 𝑏 to both sides
Factor & Simplify
Square root both sides
Solve for 𝑥

8. Solve 4 𝑥 2 −3𝑥−1=0 by completing the square
𝑥 2 − 3 4 𝑥− 1 4 =0 𝑥 2 − 3 4 𝑥 + = 𝑥− =
Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐
Add 𝑏 to both sides
Factor & Simplify
Square root both sides
Solve for 𝑥

9. Solve 4 𝑥 2 −3𝑥−1=0 by completing the square
𝑥 2 − 3 4 𝑥− 1 4 =0 𝑥 2 − 3 4 𝑥 = 𝑥− = 𝑥− 3 8 =± 5 8 𝑥= 3±5 8 𝑥=1, − 1 4
Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐
Add 𝑏 to both sides
Factor & Simplify
Square root both sides
Solve for 𝑥

10. Questions?
Completing the square is how we get the quadratic formula That will be our next review