To solve the quadratic equation \( x^2 - 96 = 4x \) by factoring, we first need to rewrite the equation in standard form \( ax^2 + bx + c = 0 \).
- Start by moving all terms to one side: \[ x^2 - 4x - 96 = 0 \]
Now, we can proceed to factor this quadratic equation.
Jedida may have made a mistake in any of the following steps:
-
Step of Moving Terms: If she did not correctly reorganize or combine the terms from \( x^2 - 96 = 4x \), then the equation would not be accurate when factoring.
-
Factoring Error: If she attempted to factor the quadratic \( x^2 - 4x - 96 \) without finding the correct factors, then she could've incorrectly identified factors that do not multiply to give \(-96\) and add up to \(-4\). The correct factors of \(-96\) that add to \(-4\) are \(-12\) and \(8\). If she did not recognize these correct factors or made an arithmetic mistake, this would lead to an invalid factorization.
Once correctly factored, the equation should look like this: \[ (x - 12)(x + 8) = 0 \]
From this factorization, we find the solutions: \[ x - 12 = 0 \quad \Rightarrow \quad x = 12 \] \[ x + 8 = 0 \quad \Rightarrow \quad x = -8 \]
In summary, the mistake could have occurred in either reorganizing the equation incorrectly or not accurately identifying the factors during the factoring process.