consider the following quadratic equations: -y^2-16y-64=0 step 2 of 2: use the discriminant, b^(2)-4ac, to determine the number of solutions of th egiven quadratic equation, then solve the quadratic equation using the formula x=(-b+\sqrt(b^(2)-4ac))/(2a)
To determine the number of solutions of the given quadratic equation, we need to calculate the discriminant, which is given by b^2 - 4ac.
In this equation, a = -1, b = -16, and c = -64.
Discriminant = (-16)^2 - 4(-1)(-64)
= 256 - 256
= 0
Since the discriminant is equal to 0, there is only one solution for this quadratic equation.
To solve the quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in the values from the given equation, we have:
x = (-(-16) ± √((-16)^2 - 4(-1)(-64))) / (2(-1))
= (16 ± √(256 - 256)) / (-2)
= (16 ± √0) / (-2)
= (16 ± 0) / (-2)
= 16 / (-2)
= -8
Therefore, the solution to the quadratic equation -y^2 - 16y - 64 = 0 is x = -8.