Comprehensive worksheet designed to help students practice solving quadratic equations by completing the square across varying difficulty levels.

Section A
1) x = -4, x = -10
2) x = 9, x = -1
3) x = -1, x = -9
4) x = 2, x = -12

Section B
1) x = -5 + √35, x = -5 - √35
2) x = -9 + 2√22, x = -9 - 2√22
3) x = 3 + 2√3, x = 3 - 2√3
4) x = (1 + √29)/2, x = (1 - √29)/2
5) x = -6 + 2√11, x = -6 - 2√11
6) x = 16 + √221, x = 16 - √221
7) x = (-3 + √105)/2, x = (-3 - √105)/2
8) x = (5 + √41)/2, x = (5 - √41)/2

Section C
1) x ≈ 2.1, x ≈ -4.1
2) x ≈ 0.5, x ≈ -4.5
3) x ≈ 3.7, x ≈ 0.3
4) x ≈ 1.4, x ≈ -3.4
5) x ≈ 1.2, x ≈ -0.2
6) x ≈ 1.9, x ≈ -0.4

Extension
A. a = 2, b = -8
B. Starting with ax² + bx + c = 0:
Divide by a: x² + (b/a)x + c/a = 0
Move constant: x² + (b/a)x = -c/a
Complete the square: x² + (b/a)x + (b/(2a))² = -c/a + (b/(2a))²
Left side is perfect square: (x + b/(2a))² = (b² - 4ac)/(4a²)
Take square root: x + b/(2a) = ±√(b² - 4ac)/(2a)
Solve for x: x = (-b ± √(b² - 4ac))/(2a)