Solve the following quadratic equation using the perfect square trinomial pattern: 49x^2=−392x−784
.(1 point)
Responses
x=4
x=784
x=−784
x=−4
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.