Question

Hyung-eun is solving quad like a Croatian x squared - 4x - 12 = 0 by grouping her work is shown below at which step does hu
Yung-eunrst make an error

Answer 1

To determine where Hyung-eun might have made an error in solving the quadratic equation \(x^2 - 4x - 12 = 0\), let's go through the typical steps of solving a quadratic equation by factoring or completing the square.

1. **Rearranging** (if necessary):
The equation is already in standard form.

2. **Factoring**:
We need to factor \(x^2 - 4x - 12\). We're looking for two numbers that multiply to \(-12\) (the constant term) and add up to \(-4\) (the coefficient of \(x\)):
The numbers that satisfy this are \(-6\) and \(2\):
\[
x^2 - 4x - 12 = (x - 6)(x + 2) = 0
\]

3. **Setting each factor to zero**:
\((x - 6) = 0\) or \((x + 2) = 0\)
This leads to:
\[
x = 6 \quad \text{or} \quad x = -2
\]

4. **Checking**:
You can verify by plugging \(x = 6\) and \(x = -2\) back into the original equation to ensure that both satisfy it.

Now, if Hyung-eun used a different method like grouping or incomplete factoring and made any algebraic mistakes along the way (such as a sign error, coefficient mistake, or miscalculation), we would need to see her specific work or steps to identify the error.

If you provide Hyung-eun's specific steps as she worked through the problem, I can help pinpoint where she first made an error.