Solve the following quadratic equation using the perfect square trinomial pattern: 49x² = -392x – 784.

Question

• X = 784
• X = -784
• X = 4
• X = -4

Answer 1

The correct answer is X = 4.

To solve the quadratic equation 49x² = -392x - 784, we can first move all the terms to one side to make it equal to zero:

49x² + 392x + 784 = 0

Next, we can divide every term by 49 to simplify the equation:

x² + 8x + 16 = 0

Now, we can see that the equation is a perfect square trinomial because the first and last terms are perfect squares (x² = (x)(x) and 16 = (4)(4)). The middle term 8x can be written as 2 * (x)(4) or 2 * (2)(2)(x), which means it is twice the product of the square root of the first term and the square root of the last term.

Therefore, we can rewrite the equation as:

(x + 4)² = 0

Taking the square root of both sides gives us:

x + 4 = 0

Subtracting 4 from both sides gives us the final answer:

x = -4

So, the solution to the quadratic equation 49x² = -392x - 784 is x = -4.