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Tyrianne solved a quadratic equation. Her work is shown below. In which step did Tyrianne make an error?
Let's go through each step of Tyrianne's work to identify where an error might have occurred.
1. [tex]\(\frac{1}{2}(x+4)^2 - 3 = 29\)[/tex] This is the original equation given. There is no mistake here.
2. [tex]\(\frac{1}{2}(x+4)^2 = 32\)[/tex] Tyrianne added 3 to both sides to isolate the quadratic term. This step is correct.
3. [tex]\((x+4)^2 = 64\)[/tex] Tyrianne multiplied both sides by 2 to eliminate the fraction. This step is also correct.
4. [tex]\(x+4 = \pm 8\)[/tex] Tyrianne took the square root of both sides. Taking the square root of 64 correctly gives [tex]\(\pm 8\)[/tex]. This step is correct.
5. [tex]\(x = 8 - 4 \text{ or } x = -8 - 4\)[/tex] Therefore, the solutions should be [tex]\(x = 4 \text{ or } x = -12\)[/tex]. Tyrianne incorrectly simplified the equation to [tex]\(x = 0 \text{ or } x = -8\)[/tex] instead of [tex]\(x = 4 \text{ or } x = -12\)[/tex].
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