Since the user options (ExplainAnswer, TeachTopic, GeneratePractice) are all set to false, I will provide only the Final Answer section with solutions to all problems on the worksheet.
Final Answer:
Section A:
1) x = -4 or x = -10
2) x = 9 or x = -1
3) x = -5 + 4√2 or x = -5 - 4√2
4) x = -4 + 6 or x = -4 - 6 → x = 2 or x = -10
Section B:
1) x = -2 ± √34
2) x = -9 ± √102
3) x = 3 ± √12 → x = 3 ± 2√3
4) x = ½ ± √(29/4) → x = ½ ± (√29)/2
5) x = -6 ± √84 → x = -6 ± 2√21
6) x = 16 ± √206
7) x = -³⁄₂ ± √(121/4) → x = -¹·⁵ ± 5.5 → x = 4 or x = -7
8) x = ⁵⁄₂ ± √(41/4) → x = ²·⁵ ± (√41)/2
Section C (rounded to one decimal place):
1) x ≈ 2.1 or x ≈ -4.1
2) x ≈ 0.5 or x ≈ -4.5
3) x ≈ 3.6 or x ≈ 0.4
4) x ≈ 1.1 or x ≈ -4.6
5) x ≈ 1.2 or x ≈ -0.2
6) x ≈ 2.2 or x ≈ -0.7
Extension:
A. a = -8, b = 12
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 square: add (b/(2a))² to both sides. Left side becomes (x + b/(2a))². Right side simplifies to (b² - 4ac)/(4a²). Take square root: x + b/(2a) = ±√(b² - 4ac)/(2a). Subtract b/(2a): x = [-b ± √(b² - 4ac)] / (2a). Proven.
Parent Tip: Review the logic above to help your child master the concept of solving quadratic equations using the quadratic formula worksheet.
