Let's solve the given equation step by step.
Given equation:
[tex]\[ 2x^2 + 16 + 32 = 0 \][/tex]
1. Combine constants:
We can simplify the equation by combining the constants 16 and 32.
[tex]\[ 2x^2 + 48 = 0 \][/tex]
2. Isolate the [tex]\(x^2\)[/tex] term:
Move the constant term 48 to the other side of the equation to isolate the [tex]\(x^2\)[/tex] term.
[tex]\[ 2x^2 = -48 \][/tex]
3. Solve for [tex]\(x^2\)[/tex]:
Divide both sides of the equation by 2 to solve for [tex]\(x^2\)[/tex].
[tex]\[ x^2 = -24 \][/tex]
4. Analyze the value of [tex]\(x^2\)[/tex]:
We notice that [tex]\(x^2 = -24\)[/tex]. Since the square of a real number [tex]\(x\)[/tex] cannot be negative (because any real number squared is non-negative), this equation has no real solutions.
Therefore, there are no real solutions to this equation. Thus, [tex]\(d\)[/tex] or the result is:
[tex]\[ d = \text{None} \][/tex]
So, the answer is [tex]\( \boxed{\text{None}} \)[/tex].
