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Question

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

x=4
x equals 4

x=−4
x equals negative 4

x=784
x equals 784

x=−784
x equals negative 784
Remaining Attempts : 3
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1 answer

To solve the quadratic equation \( 49x^2 = -392x - 784 \) using the perfect square trinomial pattern, we start by rearranging the equation into standard form.

  1. Move all terms to one side of the equation: \[ 49x^2 + 392x + 784 = 0 \]

  2. Divide the entire equation by 49 to simplify: \[ x^2 + 8x + 16 = 0 \]

  3. Notice that the left-hand side can be factored as a perfect square trinomial: \[ (x + 4)^2 = 0 \]

  4. Set the factor equal to 0: \[ x + 4 = 0 \]

  5. Solve for \( x \): \[ x = -4 \]

Thus, the solution to the equation \( 49x^2 = -392x - 784 \) is: \[ x = -4 \]

The correct response is: x equals negative 4.