Question

Which equation is equivalent to the given equation?
8, x, equals, minus, x, squared, minus, 16
8x=−x
2
−16
Answer
x, squared, minus, 8, x, minus, 16, equals, 0
x
2
−8x−16=0
x, squared, plus, 8, x, minus, 16, equals, 0
x
2
+8x−16=0
x, squared, minus, 8, x, plus, 16, equals, 0
x
2
−8x+16=0
x, squared, plus, 8, x, plus, 16, equals, 0
x
2
+8x+16=0

Answer 1

To determine which equation is equivalent to \( 8x = -x^2 - 16 \), we can rearrange the equation to set it equal to zero.

Starting with the original equation:

\[ 8x = -x^2 - 16 \]

We can add \( x^2 \) and 16 to both sides:

\[ x^2 + 8x + 16 = 0 \]

Now let's analyze the provided options:

1. \( x^2 - 8x - 16 = 0 \)
2. \( x^2 + 8x - 16 = 0 \)
3. \( x^2 - 8x + 16 = 0 \)
4. \( x^2 + 8x + 16 = 0 \)

The equation we derived, \( x^2 + 8x + 16 = 0 \), matches option 4.

Thus, the correct answer is:

\[ \boxed{x^2 + 8x + 16 = 0} \]