Question
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Tutor-Verified Answer
Answer
\( x=-35 \)
Solution
Solve the equation \( \sqrt{-x+1}-6=0 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\sqrt{-x+1}-6=0\)
- step1: Find the domain:
\(\sqrt{-x+1}-6=0,x\leq 1\)
- step2: Move the constant to the right side:
\(\sqrt{-x+1}=0+6\)
- step3: Remove 0:
\(\sqrt{-x+1}=6\)
- step4: Raise both sides to the \(2\)-th power\(:\)
\(\left(\sqrt{-x+1}\right)^{2}=6^{2}\)
- step5: Evaluate the power:
\(-x+1=36\)
- step6: Move the constant to the right side:
\(-x=36-1\)
- step7: Subtract the numbers:
\(-x=35\)
- step8: Change the signs:
\(x=-35\)
- step9: Check if the solution is in the defined range:
\(x=-35,x\leq 1\)
- step10: Find the intersection:
\(x=-35\)
- step11: Check the solution:
\(x=-35\)
The solution to the equation \( \sqrt{-x+1}-6=0 \) is \( x=-35 \).
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Simplify this solution Beyond the Answer
To solve the equation \( \sqrt{-x+1}-6=0 \), first isolate the square root on one side: \[ \sqrt{-x+1} = 6 \] Next, square both sides to eliminate the square root: \[ -x + 1 = 36 \] Now, solve for \( x \): \[ -x = 36 - 1 \] \[ -x = 35 \] \[ x = -35 \] Finally, always check your answer by substituting it back into the original equation: \[ \sqrt{-(-35)+1}-6 = \sqrt{35+1}-6 = \sqrt{36}-6 = 6-6 = 0 \] Thus, the solution to the equation is \( x = -35 \).
