What are the real solutions, if any, for −x2−3.5=−12.5 ?(1 point)

Question

Responses

{−4,4}
left brace negative 4 comma 4 right brace

{−3,3}
left brace negative 3 comma 3 right brace

There are no real solutions.
There are no real solutions.

9

Answer 1

To solve the equation \(-x^2 - 3.5 = -12.5\), we can first simplify it.

1. Add 3.5 to both sides: \[ -x^2 - 3.5 + 3.5 = -12.5 + 3.5 \] This simplifies to: \[ -x^2 = -9 \]

2. Multiply both sides by -1: \[ x^2 = 9 \]

3. Take the square root of both sides: \[ x = \pm 3 \]

Thus, the real solutions are: \[ { -3, 3 } \]

So the correct response is: \({ -3, 3 }\) (left brace negative 3 comma 3 right brace).