Solve the following quadratic equation using the perfect square trinomial pattern: 49x² = -392x – 784.
• X = 784
• X = -784
• X = 4
• X = -4
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.