Page 2: Student's Solutions

This page shows the student's (Nicole Axyonov) solutions to the given problems.

For equation a (x² - 16 = 0), the student correctly identifies the solutions as x₁ = 4 and x₂ = -4.

For equation b (x² + 5x + 6 = 0), the student uses the quadratische Gleichung lösen Formel (quadratic formula) to find the solutions x₁ = -3 and x₂ = -2.

Definition: The quadratische Gleichung lösen Formel or quadratic formula is x = [-b ± √(b² - 4ac)] / (2a), where a, b, and c are the coefficients in the standard form of a quadratic equation (ax² + bx + c = 0).

For equation c (x² + 8x - 48 = 0), the student again applies the quadratic formula, finding the solutions x₁ = 4 and x₂ = -12.

The student chooses to solve word problem W2, setting up the equation x² + x = 240 and solving it to find x = 15.98 (approximately).

Example: The solution process for W2 involves:

1. Setting up the equation: x² + x = 240
2. Rearranging to standard form: x² + x - 240 = 0
3. Applying the quadratic formula or factoring to solve

Highlight: This page demonstrates the practical application of quadratische Gleichungen Übungen (quadratic equation exercises) and showcases various methods for solving different types of quadratic equations.