Final answer:
To find the x-value of a stationary point involving a square root, isolate and perform the square root operation while considering both positive and negative roots, unless the context limits the answer to positive values only. Use your calculator for computations, knowing that square rooting is equivalent to raising to the power of 0.5.
Step-by-step explanation:
When finding the x-value of a stationary point and your answer involves a square root, you must consider both the positive and negative roots, unless the context of the problem constrains the solution to only positive values. For instance, in equilibrium problems in chemistry, negative concentrations do not make sense, so only the positive root would be considered.
Here's a step-by-step strategy to handle such problems:
- Isolate the square root expression if possible.
- Perform the square root operation on both sides of the equation.
- Remember that √x² = ±x, which means you must consider both the positive and negative values that x could represent unless the problem context indicates otherwise.
- Check the solutions in the original problem to ensure they are practical or physically possible.
- If the problem involves a square root of a negative number, remember this is not possible within the real numbers and instead introduces complex numbers.
- Use your calculator to perform the square root operation, and remember that raising to the power of 0.5 is equivalent to taking a square root. Some calculators have dedicated square root buttons, while others require you to raise the number to the power of 0.5.