Jedida solved the quadratic equation x2−96=4x

Question

by factoring. Her work is shown below. Explain what step she made a mistake and what she did wrong.
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(2 points)

Answer 1

Jedida made a mistake in Step 1 of her work. Let's break it down:

1. The original equation is \( x^2 - 96 = 4x \).

2. When she rearranged the equation, she needed to move all terms to one side in order to set the equation to zero. She correctly realized she needed to subtract \( 4x \) from both sides, but she incorrectly added \( 4x \) to the left side in her Step 1. The correct step should be:

   \[ x^2 - 4x - 96 = 0. \]

3. Therefore, the mistake was in her transition from \( x^2 - 96 = 4x \) to \( x^2 + 4x - 96 = 0 \). The correct formulation includes a negative \( 4x \) term.

4. After correcting the equation to \( x^2 - 4x - 96 = 0 \), the correct factored form would be:

   \[ (x - 12)(x + 8) = 0. \]

5. The correct solutions to the equation would then be \( x = 12 \) or \( x = -8 \) instead of \( x = -12 \) and \( x = 8 \) as concluded by Jedida.

In summary, her mistake was incorrectly adding \( 4x \) instead of subtracting it, leading to an incorrect factored equation and incorrect solutions.