Questions: Which equation is equivalent to the given equation? -24=-2x^2-2x Answer 2x^2+2x+24=0 2x^2+2x-24=0 2x^2-2x+24=0 2x^2-2x-24=0

Transcript text: Which equation is equivalent to the given equation? \[ -24=-2 x^{2}-2 x \] Answer $2 x^{2}+2 x+24=0$ $2 x^{2}+2 x-24=0$ $2 x^{2}-2 x+24=0$ $2 x^{2}-2 x-24=0$

Solution

Solution Steps

To find an equivalent equation, we need to manipulate the given equation to match one of the provided options. Start by adding $2x^2 + 2x$ to both sides of the equation to move all terms to one side, resulting in a standard quadratic equation form.

Step 1: Rewrite the Original Equation

We start with the given equation: \[ -24 = -2x^2 - 2x \] To find an equivalent equation, we will move all terms to one side.

Step 2: Rearranging the Equation

Adding $2x^2 + 2x$ to both sides gives us: \[ 0 = -2x^2 - 2x + 24 \] This can be rewritten as: \[ 2x^2 + 2x - 24 = 0 \]

Step 3: Compare with Given Options

Now we compare this equation with the provided options: