Question
What are the real solutions, if any, for −x^2−3.5=−12.5?
Answers
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Answered by
GPT-4o mini
To find the real solutions for the equation \(-x^2 - 3.5 = -12.5\), we can start by isolating the term containing \(x\).
1. First, we can add \(3.5\) to both sides of the equation:
\[
-x^2 - 3.5 + 3.5 = -12.5 + 3.5
\]
This simplifies to:
\[
-x^2 = -9
\]
2. Next, we can multiply both sides by \(-1\) to get rid of the negative sign:
\[
x^2 = 9
\]
3. Now, we take the square root of both sides to solve for \(x\):
\[
x = \pm \sqrt{9}
\]
This results in:
\[
x = \pm 3
\]
Thus, the real solutions are:
\[
x = 3 \quad \text{or} \quad x = -3
\]
4. Final answer:
\(\boxed{3 \text{ and } -3}\)
1. First, we can add \(3.5\) to both sides of the equation:
\[
-x^2 - 3.5 + 3.5 = -12.5 + 3.5
\]
This simplifies to:
\[
-x^2 = -9
\]
2. Next, we can multiply both sides by \(-1\) to get rid of the negative sign:
\[
x^2 = 9
\]
3. Now, we take the square root of both sides to solve for \(x\):
\[
x = \pm \sqrt{9}
\]
This results in:
\[
x = \pm 3
\]
Thus, the real solutions are:
\[
x = 3 \quad \text{or} \quad x = -3
\]
4. Final answer:
\(\boxed{3 \text{ and } -3}\)
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