Solve the following quadratic equation using the perfect square trinomial pattern: 49x2=−392x−784

Question

.(1 point)
Responses

x=−784
x equals negative 784

x=784
x equals 784

x=4
x equals 4

x=−4

Answer 1

To solve the quadratic equation \( 49x^2 = -392x - 784 \) using the perfect square trinomial pattern, let's first rearrange the equation:

1. Move all terms to one side of the equation:

   \[ 49x^2 + 392x + 784 = 0 \]

2. Next, we can divide the entire equation by 49 to simplify it:

   \[ x^2 + 8x + 16 = 0 \]

3. Now, notice that \( x^2 + 8x + 16 \) is a perfect square trinomial, as it can be factored as:

   \[ (x + 4)^2 = 0 \]

4. Setting the factored equation equal to zero gives us:

   \[ (x + 4)^2 = 0 \]

5. Taking the square root of both sides results in:

   \[ x + 4 = 0 \]

6. Solving for \( x \):

   \[ x = -4 \]

Thus, the solution to the quadratic equation is:

\[ \boxed{-4} \]

So, the correct response is \( x = -4 \).