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

Question

.(1 point)
Responses

x=4
x equals 4

x=−4
x equals negative 4

x=784
x equals 784

x=−784

Answer 1

To solve the given quadratic equation \(49x^2 = -392x - 784\) using the perfect square trinomial pattern, we first rearrange it into standard form:

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

Next, we can simplify this equation by dividing all terms by 49 (the coefficient of \(x^2\)):

\[ x^2 + \frac{392}{49}x + \frac{784}{49} = 0 \] \[ x^2 + 8x + 16 = 0 \]

Now, we see that the left-hand side can be expressed as a perfect square:

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

To solve for \(x\), we take the square root of both sides:

\[ x + 4 = 0 \]

Thus, solving for \(x\):

\[ x = -4 \]

The solution to the given quadratic equation is:

\[ x = -4 \]

So the correct response is:

x equals negative 4.