Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( n=-4 \)
Solution
Solve the equation \( \sqrt{1-20n}+2=11 \).
Solve the equation by following steps:
- step0: Solve for \(n\):
\(\sqrt{1-20n}+2=11\)
- step1: Find the domain:
\(\sqrt{1-20n}+2=11,n\leq \frac{1}{20}\)
- step2: Move the constant to the right side:
\(\sqrt{1-20n}=11-2\)
- step3: Subtract the numbers:
\(\sqrt{1-20n}=9\)
- step4: Raise both sides to the \(2\)-th power\(:\)
\(\left(\sqrt{1-20n}\right)^{2}=9^{2}\)
- step5: Evaluate the power:
\(1-20n=81\)
- step6: Move the constant to the right side:
\(-20n=81-1\)
- step7: Subtract the numbers:
\(-20n=80\)
- step8: Change the signs:
\(20n=-80\)
- step9: Divide both sides:
\(\frac{20n}{20}=\frac{-80}{20}\)
- step10: Divide the numbers:
\(n=-4\)
- step11: Check if the solution is in the defined range:
\(n=-4,n\leq \frac{1}{20}\)
- step12: Find the intersection:
\(n=-4\)
- step13: Check the solution:
\(n=-4\)
The solution to the equation \( \sqrt{1-20n}+2=11 \) is \( n=-4 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To solve the equation \( \sqrt{1-20n}+2=11 \), we first isolate the square root. Subtracting 2 from both sides gives us: \[ \sqrt{1-20n} = 9 \] Next, we square both sides to eliminate the square root: \[ 1-20n = 81 \] Now, we can solve for \( n \) by first subtracting 1 from both sides: \[ -20n = 80 \] Dividing by -20, we find: \[ n = -4 \] So, the solution is \( n = -4 \).
