Solve the following quadratic equation using the perfect square trinomial pattern: 49x2=−392x−784 .(1 point)

Question

Responses

x=4
x equals 4

x=784
x equals 784

x=−784
x equals negative 784

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 in standard form:

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

Next, we notice that this quadratic can be factored by identifying a perfect square trinomial. We can rewrite the left-hand side:

\[ (7x + 28)^2 = 0 \]

To see how we reached this, we recognize that:

\[ (7x + 28)(7x + 28) = 49x^2 + 392x + 784 \]

Now, we set the factor equal to zero:

\[ (7x + 28) = 0 \]

Solving for \(x\):

\[ 7x = -28 \] \[ x = -4 \]

Hence, the solution to the quadratic equation \( 49x^2 = -392x - 784 \) is:

x = -4.

Therefore, the correct response is:

x = -4.