Question
Solve this equation. If the equation has no valid solutions, click on the appropriate button. \[ \sqrt{x-4}+9=14 \]
Ask by Hills Huang. in the United States
Mar 05,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x=29 \)
Solution
Solve the equation \( \sqrt{x-4}+9=14 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\sqrt{x-4}+9=14\)
- step1: Find the domain:
\(\sqrt{x-4}+9=14,x\geq 4\)
- step2: Move the constant to the right side:
\(\sqrt{x-4}=14-9\)
- step3: Subtract the numbers:
\(\sqrt{x-4}=5\)
- step4: Raise both sides to the \(2\)-th power\(:\)
\(\left(\sqrt{x-4}\right)^{2}=5^{2}\)
- step5: Evaluate the power:
\(x-4=25\)
- step6: Move the constant to the right side:
\(x=25+4\)
- step7: Add the numbers:
\(x=29\)
- step8: Check if the solution is in the defined range:
\(x=29,x\geq 4\)
- step9: Find the intersection:
\(x=29\)
- step10: Check the solution:
\(x=29\)
The solution to the equation \( \sqrt{x-4}+9=14 \) is \( x=29 \).
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Beyond the Answer
To solve the equation \( \sqrt{x-4}+9=14 \), we first isolate the square root: 1. Subtract 9 from both sides: \[ \sqrt{x-4} = 14 - 9 \] \[ \sqrt{x-4} = 5 \] 2. Next, we square both sides to eliminate the square root: \[ x - 4 = 5^2 \] \[ x - 4 = 25 \] 3. Finally, add 4 to both sides to solve for \( x \): \[ x = 25 + 4 \] \[ x = 29 \] So, the solution to the equation is \( x = 29 \).