what is the solution set of :
x^2 + 9 = 0
to answer that i would subtract the 9 from both sides giving you x^2=-9
then i would take the square root of both sides giving x=-3
Does that make sense?
Michele's answer is not correct
x^=-9 has no solution in the set of real numbers (x=-3 is a real number solution)
You will have to use imaginary or complex numbers
x^2 = -9
x = ±√-9
x = ± 3i where i = √-1
To find the solution set for the equation x^2 + 9 = 0, we can follow these steps:
Step 1: Subtract 9 from both sides of the equation:
x^2 = -9
Step 2: Take the square root of both sides:
sqrt(x^2) = sqrt(-9)
Step 3: Since the square root of a negative number is not a real number, we cannot proceed further. Therefore, the equation x^2 + 9 = 0 has no real solutions.
In terms of complex numbers, we can rewrite the equation as:
x^2 = -9
Taking the square root of both sides:
x = ±√(-9)
Using the imaginary unit "i", where i^2 = -1, we can simplify the square root:
x = ±3i
So, the solution set for x^2 + 9 = 0 is {3i, -3i}.
To find the solution set of the equation x^2 + 9 = 0, we need to solve for x.
Step 1: Begin by subtracting 9 from both sides of the equation:
x^2 = -9
Step 2: Take the square root of both sides of the equation. Remember that the square root of a negative number is not a real number, so we need to use the imaginary unit 'i' to represent the square root of -1:
√(x^2) = ±√(-9)
x = ±√(-9)
Step 3: Simplify the expression √(-9) by factoring -9.
√(x^2) = ±√(-1 * 3^2)
x = ±3i√1
Therefore, the solution set of the equation x^2 + 9 = 0 is x = ±3i.