Answer:
Certainly! I'd be happy to help you solve this equation.
First, let's start by simplifying the equation:
8w^2 + 1 = -8w
We can start by subtracting 1 from both sides of the equation:
8w^2 = -9w
Now, we can factor the left-hand side of the equation:
8w^2 = 2(2w)^2
Since 2w is a perfect square (2w = √(4w^2)), we can rewrite the equation as:
2(2w)^2 = -9w
Simplifying further:
2(4w^2) = -9w
4w^2 = -9w/2
w^2 = (-9w/2)/4
w^2 = (-9/8)w
The solution to the equation is:
w = ±√(-9/8)
BOLD answer: √(-9/8)
Explanation: