Answer :
To solve the equation [tex]\(x^2 = -49\)[/tex], let's break it down step by step:
1. Understand the equation: The equation [tex]\(x^2 = -49\)[/tex] means we are looking for a number [tex]\(x\)[/tex] such that when you square it (multiply it by itself), you get -49.
2. Consider the properties of squaring: In real numbers, when you square any real number, the result is always non-negative. This means the smallest value [tex]\(x^2\)[/tex] can be is 0 (if [tex]\(x = 0\)[/tex]), and it can get larger for other real numbers, but it cannot become negative.
3. Analyze the given equation: Given that [tex]\(x^2 = -49\)[/tex], we need a number that when squared equals a negative number, which contradicts the property that squaring a real number results in a non-negative number.
4. Conclusion for real solutions: Since there is no real number that can satisfy [tex]\(x^2 = -49\)[/tex], this equation has no solution in the real number system.
Thus, the correct choice from the options given is F. None, because there are no real solutions to the equation.
1. Understand the equation: The equation [tex]\(x^2 = -49\)[/tex] means we are looking for a number [tex]\(x\)[/tex] such that when you square it (multiply it by itself), you get -49.
2. Consider the properties of squaring: In real numbers, when you square any real number, the result is always non-negative. This means the smallest value [tex]\(x^2\)[/tex] can be is 0 (if [tex]\(x = 0\)[/tex]), and it can get larger for other real numbers, but it cannot become negative.
3. Analyze the given equation: Given that [tex]\(x^2 = -49\)[/tex], we need a number that when squared equals a negative number, which contradicts the property that squaring a real number results in a non-negative number.
4. Conclusion for real solutions: Since there is no real number that can satisfy [tex]\(x^2 = -49\)[/tex], this equation has no solution in the real number system.
Thus, the correct choice from the options given is F. None, because there are no real solutions to the equation.
