Section A
1) x = -4, x = -10
2) x = 9, x = -1
3) x = -1, x = -9
4) x = 2, x = -10
Section B
1) x = -2 + √34, x = -2 - √34
2) x = -9 + √102, x = -9 - √102
3) x = 3 + 2√3, x = 3 - 2√3
4) x = 1/2 + √29/2, x = 1/2 - √29/2
5) x = -6 + √64, x = -6 - √64 → x = 2, x = -14
6) x = 16 + √216, x = 16 - √216 → x = 16 + 6√6, x = 16 - 6√6
7) x = -3/2 + √109/2, x = -3/2 - √109/2
8) x = 5/2 + √61/2, x = 5/2 - √61/2
Section C
1) x ≈ 2.2, x ≈ -4.2
2) x ≈ 0.5, x ≈ -4.5
3) x ≈ 3.6, x ≈ 0.4
4) x ≈ 1.4, x ≈ -3.7
5) x ≈ 1.2, x ≈ -0.2
6) x ≈ 2.2, x ≈ -0.7
Extension
A. a = -8, b = 5
B. Proof:
Start 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 becomes (x + b/(2a))² = (b² - 4ac)/(4a²).
Take square root: x + b/(2a) = ±√(b² - 4ac)/(2a).
Solve for x: x = (-b ± √(b² - 4ac)) / (2a).
Parent Tip: Review the logic above to help your child master the concept of completing the square practice worksheet.
