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, we can first rearrange the equation to standard form:

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

Next, we divide the entire equation by \(49\) to simplify it:

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

Now we notice that \(x^2 + 8x + 16\) can be factored as a perfect square trinomial:

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

Taking the square root of both sides gives us:

\[ x + 4 = 0 \]

Solving for \(x\):

\[ x = -4 \]

Thus, the solution to the quadratic equation is:

\[ \boxed{-4} \]