Wyatt Blake
03/09/2023 · Elementary School
9. \( \sqrt{s-27}+\sqrt{s}=9 \)
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Step-by-step Solution
Solve the equation \( \sqrt{s-27}+\sqrt{s}=9 \).
Solve the equation by following steps:
- step0: Solve for \(s\):
\(\sqrt{s-27}+\sqrt{s}=9\)
- step1: Find the domain:
\(\sqrt{s-27}+\sqrt{s}=9,s\geq 27\)
- step2: Move the expression to the right-hand side:
\(\sqrt{s-27}=9-\sqrt{s}\)
- step3: Evaluate:
\(\sqrt{s-27}=9-\sqrt{s},9-\sqrt{s}\geq 0\)
- step4: Evaluate:
\(\sqrt{s-27}=9-\sqrt{s},s\leq 81\)
- step5: Solve the equation:
\(s=36,s\leq 81\)
- step6: Find the intersection:
\(s=36\)
- step7: Check if the solution is in the defined range:
\(s=36,s\geq 27\)
- step8: Find the intersection:
\(s=36\)
- step9: Check the solution:
\(s=36\)
The solution to the equation \( \sqrt{s-27}+\sqrt{s}=9 \) is \( s=36 \).
Quick Answer
\( s=36 \)
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