how many real number solutions does the equation have?

-8x^2-8x-2=0

the answer is 1, but why

please and thank you

2 answers

divide by -2 ... 4 x^2 + 4 x + 1 = 0

factoring ... (2 x + 1)(2 x + 1) = 0

it's a perfect square
The number of solutions tells you how many times the function
touches or crosses the x-axis.

h = Xv = -B/2A = 8/-16 = -1/2.
Plug -1/2 into the given Eq. and get Y = 0.
V(-1/2, 0).

The parabola touches the x-axis at the vertex only.
If the vertex was above the x-axis, we'll have 2 solutions.