Ask a New Question
Menu

Jedida solved the quadratic equation x2−96=4x by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?

x2−96=4x
Step 1: x2+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
(1 point)

3 answers

Jedida's work contains a mistake in Step 1.

The original equation is given as:

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

To rewrite it in standard form \(ax^2 + bx + c = 0\), you would need to set it equal to zero. The correct transformation should be:

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

Instead, Jedida wrote:

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

This is incorrect because she incorrectly added \(4x\) to the left side of the equation, leading to the wrong quadratic equation.

Thus, the first mistake occurred in Step 1, where she incorrectly set up \(x^2 + 4x - 96 = 0\). The correct setup should have been \(x^2 - 4x - 96 = 0\).

Jedida solved the quadratic equation x2−96=4x by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?

x2−96=4x
Step 1: x2+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
(1 point)
Responses

Step 3; she did not apply the Zero Product Property correctly.
Step 3; she did not apply the Zero Product Property correctly.

Step 1; she added 4x to both sides instead of subtracting.
Step 1; she added 4 x to both sides instead of subtracting.

Step 2; she did not factor the left side of the equation correctly.
Step 2; she did not factor the left side of the equation correctly.

She did not make any mistakes.

Jedida’s first mistake occurred in Step 1.

In that step, she incorrectly modified the original equation by adding \(4x\) to both sides. The correct action should have been to subtract \(4x\) from both sides in order to properly set the quadratic equation to zero:

The original equation is:

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

This should be rewritten as:

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

Instead, Jedida incorrectly wrote:

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

This is where she made the mistake.

So, the correct response is:

Step 1; she added 4x to both sides instead of subtracting.