Ayala Martin
04/06/2023 · Primary School
he problem \( \sqrt{x-5}-\sqrt{2 x+7}=-3 \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( \sqrt{x-5}-\sqrt{2x+7}=-3 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\sqrt{x-5}-\sqrt{2x+7}=-3\)
- step1: Find the domain:
\(\sqrt{x-5}-\sqrt{2x+7}=-3,x\geq 5\)
- step2: Move the expression to the right-hand side:
\(\sqrt{x-5}=-3+\sqrt{2x+7}\)
- step3: Evaluate:
\(\sqrt{x-5}=-3+\sqrt{2x+7},-3+\sqrt{2x+7}\geq 0\)
- step4: Evaluate:
\(\sqrt{x-5}=-3+\sqrt{2x+7},x\geq 1\)
- step5: Solve the equation:
\(\begin{align}&x=21\\&x=9\end{align},x\geq 1\)
- step6: Find the intersection:
\(\begin{align}&x=21\\&x=9\end{align}\)
- step7: Check if the solution is in the defined range:
\(\begin{align}&x=21\\&x=9\end{align},x\geq 5\)
- step8: Find the intersection:
\(\begin{align}&x=21\\&x=9\end{align}\)
- step9: Check the solution:
\(\begin{align}&x=21\\&x=9\end{align}\)
- step10: Rewrite:
\(x_{1}=9,x_{2}=21\)
The solutions to the equation \( \sqrt{x-5}-\sqrt{2x+7}=-3 \) are \( x=9 \) and \( x=21 \).
Quick Answer
The solutions are \( x=9 \) and \( x=21 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit