Quadratic Formula Find the discriminant of the following equations and use it to determine the number and type of solutions. 8. -x^2-6x-9=0

## Step 1: Identify the coefficients<br />### The given equation is $-x^2 - 6x - 9 = 0$. Here, $a = -1$, $b = -6$, and $c = -9$.<br /><br />## Step 2: Calculate the discriminant<br />### The discriminant is given by the formula $\Delta = b^2 - 4ac$. Substituting the values, we get $\Delta = (-6)^2 - 4(-1)(-9) = 36 - 36 = 0$.<br /><br />## Step 3: Analyze the discriminant<br />### Since the discriminant $\Delta = 0$, the quadratic equation has one real solution (a repeated root).