Jedida solved the quadratic equation x2−96=4x

Question

by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?

x^2−96=4x

Step 1: x^2+4x−96=0
Add 4x
to both sides.
Step 2: (x+12)(x−8)=0
Factor.
Step 3: x+12=0
or x−8=0
Use the Zero Product Property.
x=−12
or x=8

Answer 1

Let's analyze Jedida's steps to find any mistakes in her work when solving the equation \( x^2 - 96 = 4x \).

Step 1: Start with the equation and rearrange it.
The original equation is: \[ x^2 - 96 = 4x \] To move \( 4x \) to the left side, we can rewrite it as: \[ x^2 - 4x - 96 = 0 \] Jedida instead wrote: \[ x^2 + 4x - 96 = 0 \] This is where she made her first mistake by incorrectly changing the sign of \( 4x \). Therefore, Step 1 itself contains an error.

Step 2: Factor the expression (incorrectly based on the first mistake).
Jedida factored \(x^2 + 4x - 96\) as \((x + 12)(x - 8) = 0\). But since Step 1 was incorrect, her factoring is also unjustified.

Step 3: Solve for \(x\).
From her incorrect factorization, she applies the Zero Product Property by setting each factor to zero. However, since her previous work was flawed, the solutions \(x = -12\) and \(x = 8\) are also incorrect.

Thus, the first mistake occurred in Step 1, where she incorrectly wrote \(x^2 + 4x - 96 = 0\) instead of the correct form \(x^2 - 4x - 96 = 0\).