Question
\( 1 \leftarrow \quad \) Solve. \( \quad-\sqrt{10 x}+1=-9 \)
Ask by Schofield Simmons. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x=10 \)
Solution
Solve the equation \( -\sqrt{10x}+1=-9 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(-\sqrt{10x}+1=-9\)
- step1: Find the domain:
\(-\sqrt{10x}+1=-9,x\geq 0\)
- step2: Move the constant to the right side:
\(-\sqrt{10x}=-9-1\)
- step3: Subtract the numbers:
\(-\sqrt{10x}=-10\)
- step4: Divide both sides:
\(\sqrt{10x}=10\)
- step5: Raise both sides to the \(2\)-th power\(:\)
\(\left(\sqrt{10x}\right)^{2}=10^{2}\)
- step6: Evaluate the power:
\(10x=100\)
- step7: Divide both sides:
\(\frac{10x}{10}=\frac{100}{10}\)
- step8: Divide the numbers:
\(x=10\)
- step9: Check if the solution is in the defined range:
\(x=10,x\geq 0\)
- step10: Find the intersection:
\(x=10\)
- step11: Check the solution:
\(x=10\)
The solution to the equation \(-\sqrt{10x}+1=-9\) is \(x=10\).
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Extra Insights
To solve the equation \( -\sqrt{10x} + 1 = -9 \), first isolate the square root term. Subtract 1 from both sides: \(-\sqrt{10x} = -10\) Now, multiply both sides by -1 to eliminate the negative sign: \(\sqrt{10x} = 10\) Next, square both sides to remove the square root: \(10x = 100\) Finally, divide both sides by 10 to solve for \(x\): \(x = 10\) So, the solution is \(x = 10\).