Pregunta
\( \mid \leftarrow \quad \) Solve. \( \quad-\sqrt{10 x}+1=-9 \)
Ask by Santiago Bond. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( x = 10 \)
Solución
We start with the equation:
\[
-\sqrt{10x} + 1 = -9
\]
**Step 1:** Subtract \(1\) from both sides.
\[
-\sqrt{10x} = -9 - 1 = -10
\]
**Step 2:** Multiply both sides by \(-1\).
\[
\sqrt{10x} = 10
\]
**Step 3:** Square both sides to eliminate the square root.
\[
10x = 10^2 = 100
\]
**Step 4:** Solve for \(x\).
\[
x = \frac{100}{10} = 10
\]
**Verification:** Substitute \(x = 10\) into the original equation.
\[
-\sqrt{10 \times 10} + 1 = -\sqrt{100} + 1 = -10 + 1 = -9
\]
The equation holds true, so the solution is correct.
\[
\boxed{x = 10}
\]
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Simplifique esta solución Beyond the Answer
To solve the equation \(-\sqrt{10x} + 1 = -9\), first, isolate the square root term. Subtract 1 from both sides: \(-\sqrt{10x} = -10\). Next, multiply both sides by -1: \(\sqrt{10x} = 10\). Now, square both sides to eliminate the square root: \(10x = 100\). Finally, divide both sides by 10 to solve for \(x\): \(x = 10\). So, the solution is \( x = 10 \). To ensure it’s correct, substitute \(x = 10\) back into the original equation: \(-\sqrt{10(10)} + 1 = -9 \implies -\sqrt{100} + 1 = -9 \implies -10 + 1 = -9\), which is true. Therefore, \(x = 10\) is indeed the correct solution!
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