What are the solutions to the equation: x² - 10?

Rationale

±√10 are the solutions to the equation: x² - 10 = 0.

To find the solutions to the equation x² - 10 = 0, we first isolate x² by adding 10 to both sides, resulting in x² = 10. Taking the square root of both sides gives us the solutions ±√10.

A (±5) YOUR ANSWER

Taking the square root of 25 yields ±5, which does not satisfy the original equation x² - 10 = 0. Since 5² equals 25, this choice does not correspond to the correct solutions derived from x² = 10.

B (±√10) CORRECT

This choice accurately represents the solutions to the equation x² - 10 = 0. By taking the square root of both sides of the equation x² = 10, we obtain ±√10, which are the correct values of x that satisfy the equation.

C (±10) YOUR ANSWER

This choice suggests that the solutions are ±10, but this is incorrect. The square of ±10 equals 100, which does not solve the original equation x² - 10 = 0. Thus, ±10 cannot be correct solutions.

D (±10²) YOUR ANSWER

This choice implies ±100, as 10² equals 100. Since ±100 does not satisfy the equation x² - 10 = 0 (where we need x² to equal 10), this option does not provide the correct solutions.

E (±20) YOUR ANSWER

Choosing ±20 implies that the solutions are 20 or -20. However, 20² equals 400, which is not equal to 10. Therefore, ±20 cannot be the correct answers to the equation x² - 10 = 0.

Conclusion

The solutions to the equation x² - 10 = 0 are correctly given by ±√10, which results from isolating x² and taking the square root. All other choices either misinterpret the equation or provide incorrect values that do not satisfy the condition x² = 10. Thus, recognizing the correct mathematical procedure leads us to the accurate solutions of the equation.