Simplify this

Question

Jamal's Solution
Original Equation:
Factoring: Correctly factors to .
Zero Product Property: Sets each factor equal to zero:
→
→
Conclusion: Both solutions and are correct.
George's Solution
Original Equation:
Misstep: Did not set the equation to zero; incorrectly attempted to factor.
Incorrectly factors as .
Zero Product Property: Incorrectly applies the zero product property:
Results in → and → .
Conclusion: and are incorrect.
Correct Approach for George's Equation
Set to Zero: Start with .
Rearrange to by subtracting 7 from both sides.
Factoring: Factor to .
Apply Zero Product Property:
Set →
Set → .
Conclusion: The correct solutions are and .
Summary
Jamal followed the correct steps to solve his equation successfully.
George's initial method was flawed due to not setting the equation equal to zero, leading to incorrect factors and roots.
By applying the correct approach, George could arrive at the same solutions as Jamal.

Answer 1

Simplified Summary of the Solutions:

Jamal's Solution:

1. Original Equation: Starts with the equation.
2. Factoring: Correctly factors it.
3. Zero Product Property: Sets each factor equal to zero leading to two solutions.
4. Conclusion: Both solutions are correct.

George's Solution:

1. Original Equation: Starts with the same equation.
2. Misstep: Fails to set the equation to zero and incorrectly attempts to factor.
3. Incorrect Factoring: Wrongly factors the equation.
4. Zero Product Property: Misapplies it, leading to incorrect results.
5. Conclusion: Both solutions he derived are incorrect.

Correct Approach for George's Equation:

1. Set to Zero: Start with the equation and rearrange it to set it equal to zero.
2. Factoring: Factor correctly.
3. Apply Zero Product Property: Set each factor to zero and solve.
4. Conclusion: Arrive at the correct solutions.

Summary:

• Jamal’s method is correct and yields true solutions.
• George’s method is flawed due to not setting the equation to zero, which leads to incorrect results.
• By following the proper method, George could achieve the same correct solutions as Jamal.