To determine the number of real number solutions to the equation 8x² + 8x² = 0, we first simplify it.
Combining like terms, we have:
16x² = 0
Next, we set the equation equal to zero:
16x² = 0
Now, we can divide both sides by 16 (since 16 is non-zero):
x² = 0
Taking the square root of both sides gives us:
x = 0
This indicates that there is only one real solution, which is x = 0.
Thus, the answer is: a) one solution.