Answer :
To solve the equation [tex]\(x^2 = -49\)[/tex], we need to determine which value or values of [tex]\(x\)[/tex] satisfy it.
1. Understanding the equation: The equation we have is [tex]\(x^2 = -49\)[/tex]. This means we're looking for a real number [tex]\(x\)[/tex] such that when squared, it equals [tex]\(-49\)[/tex].
2. Analyzing possibilities: In real numbers, the square of any real number is always non-negative (either positive or zero). For example, the square of negative numbers is positive, and the square of positive numbers is also positive. Zero squared is zero. Therefore, there is no real number whose square can result in a negative value like [tex]\(-49\)[/tex].
3. Checking the provided options:
- [tex]\(x = 0\)[/tex]: [tex]\(0^2 = 0\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
- [tex]\(x = 7\)[/tex]: [tex]\(7^2 = 49\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
- [tex]\(x = 49\)[/tex]: [tex]\(49^2 = 2401\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
- [tex]\(x = -7\)[/tex]: [tex]\((-7)^2 = 49\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
- [tex]\(x = -49\)[/tex]: [tex]\((-49)^2 = 2401\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
4. Conclusion: Since none of these values, when squared, equal [tex]\(-49\)[/tex], there are no real solutions to the equation [tex]\(x^2 = -49\)[/tex].
Therefore, the correct choice is:
F. None
1. Understanding the equation: The equation we have is [tex]\(x^2 = -49\)[/tex]. This means we're looking for a real number [tex]\(x\)[/tex] such that when squared, it equals [tex]\(-49\)[/tex].
2. Analyzing possibilities: In real numbers, the square of any real number is always non-negative (either positive or zero). For example, the square of negative numbers is positive, and the square of positive numbers is also positive. Zero squared is zero. Therefore, there is no real number whose square can result in a negative value like [tex]\(-49\)[/tex].
3. Checking the provided options:
- [tex]\(x = 0\)[/tex]: [tex]\(0^2 = 0\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
- [tex]\(x = 7\)[/tex]: [tex]\(7^2 = 49\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
- [tex]\(x = 49\)[/tex]: [tex]\(49^2 = 2401\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
- [tex]\(x = -7\)[/tex]: [tex]\((-7)^2 = 49\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
- [tex]\(x = -49\)[/tex]: [tex]\((-49)^2 = 2401\)[/tex]. This is not equal to [tex]\(-49\)[/tex].
4. Conclusion: Since none of these values, when squared, equal [tex]\(-49\)[/tex], there are no real solutions to the equation [tex]\(x^2 = -49\)[/tex].
Therefore, the correct choice is:
F. None
