Solve the following quadratic equation using the perfect square trinomial pattern: 49x^2=−392x−784

Question

.(1 point)
Responses

x=4

x=784

x=−784

x=−4

Answer 1

To solve the quadratic equation 49x^2=−392x−784 using the perfect square trinomial pattern, we first need to rearrange the equation in standard form as follows:

49x^2 + 392x + 784 = 0

Now, we can factor out the common factor of 49 from the first two terms:

49(x^2 + 8x) + 784 = 0

Next, we need to complete the square. To do this, we take half of the coefficient of the x term (which is 8) and square it:

(8/2)^2 = 4^2 = 16

We add this value to both sides of the equation:

49(x^2 + 8x + 16) + 784 + 49(16) = 49(16)

This simplifies to:

49(x + 4)^2 + 784 + 784 = 784

49(x + 4)^2 + 1568 = 784

Subtract 1568 from both sides:

49(x + 4)^2 = -784

Divide by 49:

(x + 4)^2 = -16

Now, we take the square root of both sides:

x + 4 = ±√(-16)

√(-16) is not a real number, so the equation has no real solutions. Therefore, none of the given responses are correct.