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

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

9
9

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

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

To solve the equation \(-x^2 - 3.5 = -12.5\), let's first isolate the term involving \(x\):

  1. Start by adding \(3.5\) to both sides of the equation: \[ -x^2 = -12.5 + 3.5 \] \[ -x^2 = -9 \]

  2. Now, multiply both sides by \(-1\): \[ x^2 = 9 \]

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

Thus, the solutions are \(x = -3\) and \(x = 3\), which can be expressed as the set \({-3, 3}\).

The correct answer is: \({−3,3}\)