1. Solve the equation $x^2+14x=-24$. Then look at the following worked solution (with errors) and find and describe the error or errors in the worked solution.

$\begin{array}{ccc}\hfill x^2+14x& =-24\hfill & \hfill \text{ Step 1 }\\ \hfill x^2+14x+28& =4\hfill & \hfill \text{ Step 2 }\\ \hfill (x+7{)}^2& =4\hfill & \hfill \text{ Step 3 }\\ \hfill x+7& =2\hfill & \hfill \text{ Step 4 }\\ \hfill x+7& =-2\hfill & \hfill \text{ Step 5 }\\ \hfill x& =-5\text{ and }x=9\hfill & \hfill \text{ Step 6 }\end{array}$

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$x=-2$ and $x=-12$

a. Where was the error made in the worked solution above and what was the error?

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Error: In Step 2, the number being added, 28, is not a perfect square. It should be 49.

2. Solve the equation $x^2-10x+16=0$. Then look at the following worked solution (with errors) and find and describe the error or errors in the worked solution.

$\begin{array}{ccc}\hfill x^2-10x+16& =0\hfill & \hfill \text{ Step 1 }\\ \hfill x^2-10x+25& =9\hfill & \hfill \text{ Step 2 }\\ \hfill (x-5{)}^2& =9\hfill & \hfill \text{ Step 3 }\\ \hfill x-5& =9\hfill & \hfill \text{ Step 4 }\\ \hfill x-5& =-9\hfill & \hfill \text{ Step 5 }\\ \hfill x=14& \text{ and }x=-4\hfill & \hfill \text{ Step 6 }\end{array}$

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$x=8$ and $x=2$

a. Where was the error made in the worked solution above and what was the error?

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Errors: Step 4 should have 3 on the right side, not 9. Step 5 should have -3 on the right side, not -9.

3. Solve the equation $x^2+2.4x=-0.8$. Then look at the following worked solution (with errors) and find and describe the error or errors in the worked solution.

$\begin{array}{cc}\hfill x^2+2.4x=-0.8\text{ Step 1}& \hfill \\ \hfill x^2+2.4x+1.44=0.64\text{Step 2}& \hfill \\ \hfill (x+1.2{)}^2=0.64\text{Step 3}& \hfill \\ \hfill x+1.2=0.8\text{Step 4}& \hfill \end{array}$

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$x=-0.4$ and $x=-2$

a. Where was the error made in the worked solution above and what was the error?

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Error: In Step 4, only the positive square root is written and the negative square root is neglected.

4. Solve the equation $x^2-\frac{6}{5}x+\frac{1}{5}=0$. Then look at the following worked solution (with errors) and find and describe the error or errors in the worked solution.

$\begin{array}{ccc}\hfill x^2-\frac{6}{5}x+\frac{1}{5}& \hfill =0& \hfill \text{ Step 1 }\\ \hfill x^2-\frac{6}{5}x+\frac{9}{25}& \hfill =\frac{9}{25}& \hfill \text{ Step 2 }\\ \hfill {(x-\frac{3}{5})}^2& \hfill =\frac{9}{25}& \hfill \text{ Step 3 }\\ \hfill x-\frac{3}{5}& \hfill =\frac{3}{5}& \hfill \text{ Step 4 }\\ \hfill x-\frac{3}{5}& \hfill =-\frac{3}{5}& \hfill \text{ Step 5 }\\ \hfill x=\frac{6}{5}& \hfill \text{ and }x=0& \hfill \text{ Step 6 }\end{array}$

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$x=1$ and $x=\frac{1}{5}$

a. Where was the error made in the worked solution above and what was the error?

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Errors: For example: In Step 2, different amounts are added to each side. On the left, $\frac{4}{25}$ is added. On the right, $\frac{9}{25}$ is added. Or: While $\frac{9}{25}$ is added on the right side, $\frac{1}{5}$ was only subtracted from the left side. Other explanations may also be accurate.