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Answer
There are no real solutions for \( x \) in the equation \( \sqrt{2x+5}+9=0 \).
Solution
Solve the equation \( \sqrt{2x+5}+9=0 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\sqrt{2x+5}+9=0\)
- step1: The statement is false for any value of \(x:\)
\(x \notin \mathbb{R}\)
The equation \( \sqrt{2x+5}+9=0 \) does not have any real solutions. Therefore, there is no real value of \( x \) that satisfies this equation.
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Simplify this solution Beyond the Answer
To solve the equation \( \sqrt{2x+5}+9=0 \), we first isolate the square root by subtracting 9 from both sides: \[ \sqrt{2x+5} = -9 \] However, the square root of any real number cannot be negative. Therefore, there are no real solutions to the equation. It's a reminder that sometimes equations can lead us to impossible scenarios! On a side note, if you ever encounter a similar equation, remember to check if the expression under the square root could potentially yield valid solutions in the real number system—just as we did here!
