Mitchell Norris
08/14/2023 · Senior High School
What is the solution of \( \sqrt{2 x+4}=16 ? \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( \sqrt{2x+4}=16 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\sqrt{2x+4}=16\)
- step1: Find the domain:
\(\sqrt{2x+4}=16,x\geq -2\)
- step2: Raise both sides to the \(2\)-th power\(:\)
\(\left(\sqrt{2x+4}\right)^{2}=16^{2}\)
- step3: Evaluate the power:
\(2x+4=256\)
- step4: Move the constant to the right side:
\(2x=256-4\)
- step5: Subtract the numbers:
\(2x=252\)
- step6: Divide both sides:
\(\frac{2x}{2}=\frac{252}{2}\)
- step7: Divide the numbers:
\(x=126\)
- step8: Check if the solution is in the defined range:
\(x=126,x\geq -2\)
- step9: Find the intersection:
\(x=126\)
- step10: Check the solution:
\(x=126\)
The solution to the equation \( \sqrt{2x+4}=16 \) is \( x=126 \).
Quick Answer
\( x=126 \).
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