Activity
Here are four equations followed by worked solutions of the equations. Each solution has at least one error.
1. Solve the equation . Then look at the following worked solution (with errors) and find and describe the error or errors in the worked solution.
Compare your answer:
and
Here are four equations followed by worked solutions of the equations. Each solution has at least one error.
a. Where was the error made in the worked solution above and what was the error?
Compare your answer:
Error: In Step 2, the number being added, 28, is not a perfect square. It should be 49.
2. Solve the equation . Then look at the following worked solution (with errors) and find and describe the error or errors in the worked solution.
Compare your answer:
and
a. Where was the error made in the worked solution above and what was the error?
Compare your answer:
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 . Then look at the following worked solution (with errors) and find and describe the error or errors in the worked solution.
Compare your answer:
and
a. Where was the error made in the worked solution above and what was the error?
Compare your answer:
Error: In Step 4, only the positive square root is written and the negative square root is neglected.
4. Solve the equation . Then look at the following worked solution (with errors) and find and describe the error or errors in the worked solution.
Compare your answer:
and
a. Where was the error made in the worked solution above and what was the error?
Compare your answer:
Errors: For example: In Step 2, different amounts are added to each side. On the left, is added. On the right, is added. Or: While is added on the right side, was only subtracted from the left side. Other explanations may also be accurate.
Self Check
Additional Resources
Spotting the Error When Solving Quadratics
To find the error when solving quadratics, it is helpful to first solve the problem on your own.
Solve the quadratic equation by completing the square and finding its zeros. Identify the error in the worked solution below.
Now, find the error by working through the problem and comparing steps:
In Step 3, 25 was added to the left side of the equation, but 25 was SUBTRACTED from the right side of the equation. Equations must remain balanced, and 25 should be added to each side of the equation.
Try it
Try It: Spotting the Error When Solving Quadratics
Examine the steps below and identify the error in solving the quadratic equation by completing the square:
Here is how to find the error when completing the square:
Work through the steps on your own and compare:
The error occurred in Step 5 when the plus-minus sign was not included after taking the square root of each side. This led to the second possible equation not being written.