−x2 − 10x − 16 = 0

Sure, let's solve the quadratic equation step by step.

The given equation is −x^2 − 10x − 16 = 0.

Step 1: Rewrite the equation in standard form. The standard form of a quadratic equation is ax^2 + bx + c = 0. So, our equation becomes -x^2 - 10x - 16 = 0.

Step 2: To make the equation easier to solve, let's multiply the entire equation by -1 to get rid of the negative sign in front of x^2. This gives us x^2 + 10x + 16 = 0.

Step 3: Now, we can solve the equation by factoring. We need to find two numbers that multiply to 16 and add to 10. The numbers 8 and 2 satisfy these conditions. So, we can write the equation as (x + 8)(x + 2) = 0.

Step 4: Set each factor equal to zero and solve for x. This gives us x + 8 = 0 and x + 2 = 0. Solving these equations gives us x = -8 and x = -2.

So, the solutions to the equation −x^2 − 10x − 16 = 0 are x = -8 and x = -2.