To determine which student's solution is accurate, we need to analyze the steps taken by both Jamal and George in solving the quadratic equation \(x^2 + 4x - 5 = 7\).
First, we should rewrite George's equation \(x^2 + 4x - 5 = 7\) in standard form:
- Subtract 7 from both sides: \[ x^2 + 4x - 5 - 7 = 0 \implies x^2 + 4x - 12 = 0 \]
Now we can evaluate both students based on the original equation:
1. Jamal's Solution:
- Jamal correctly rewrote the equation as \(x^2 + 4x - 12 = 0\).
- He factored it correctly into \((x + 6)(x - 2) = 0\).
- Jamal then set each factor equal to zero:
- \(x + 6 = 0 \implies x = -6\)
- \(x - 2 = 0 \implies x = 2\)
Therefore, Jamal has correctly applied the Zero Product Property after moving all terms to one side.
2. George's Solution:
- George started with the equation \(x^2 + 4x - 5 = 7\) but did not bring it to the correct standard form \(x^2 + 4x - 12 = 0\). He incorrectly wrote it as \((x + 5)(x - 1) = 7\), which is not the correct factorization of the standard form.
- Because he did not solve the equation correctly, applying the Zero Product Property to his incorrect factors leads to erroneous solutions: \(x = -5\) and \(x = 1\).
Conclusion: Jamal's solution is accurate because he properly transformed the equation into standard form \(x^2 + 4x - 12 = 0\) and factored it correctly. In contrast, George's solution is inaccurate because he did not correctly rearrange the equation before factoring, resulting in an incorrect application of the Zero Product Property. This analysis demonstrates that Jamal’s approach and final solutions of \(x = -6\) and \(x = 2\) are valid, while George’s conclusions are based on an incorrect factorization and thus are invalid.