solve for x:
-3(x^2+2)=102
-3(x^2+2)=102
x^2 + 2 = -34
x^2 = -36
x = ±6i , where i is the complex number √-1
-3(x^2+2)=102
x^2+2=102/-3
x^2=-34-2
x=sqrt32
To solve for x in the given equation -3(x^2+2) = 102, we can follow these steps:
Step 1: Distribute -3 to the terms inside the parentheses.
-3 * x^2 - 3 * 2 = 102
Simplified equation: -3x^2 - 6 = 102
Step 2: Move the constant term (-6) to the other side of the equation by adding 6 to both sides.
-3x^2 = 102 + 6
Simplified equation: -3x^2 = 108
Step 3: Divide both sides of the equation by -3 to isolate the variable x.
(-3x^2) / -3 = 108 / -3
Simplified equation: x^2 = -36
Step 4: Take the square root of both sides to solve for x.
√(x^2) = √(-36)
Simplified equation: x = ±√(-36)
Step 5: The square root of a negative number is not a real number, so the solution is imaginary. In this case, x is not a real number, and there is no real solution to the equation -3(x^2+2) = 102.