Let's take a look at Sehyr's work step by step to identify the error and find the correct solution to the equation \( w^2 - 7 = 11 \).
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Starting with the given equation: \[ w^2 - 7 = 11 \]
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Sehyr correctly added 7 to both sides: \[ w^2 - 7 + 7 = 11 + 7 \] This simplifies to: \[ w^2 = 18 \]
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Here's where Sehyr made an error. She incorrectly divided \( w^2 \) by 2, which she does not need to do. The next step should be to take the square root of both sides to solve for \( w \).
The correct step is: \[ w = \pm \sqrt{18} \]
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We can simplify \(\sqrt{18}\): \[ \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} \]
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Therefore, the correct solutions are: \[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2} \]
The solution to the equation is \(\pm 3\sqrt{2}\).
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