Answer: The two numbers that multiply to -65 and add to -8 are -13 and 5.
Steps: Here are the steps to find two numbers that multiply to -65 and add to -8:
Write down the equation x * y = -65 where x and y are the two numbers you’re looking for.
Write down the equation x + y = -8.
Solve for one of the variables in one of the equations. For example, solving for x in the second equation gives us x = -8 - y.
Substitute this expression for x into the first equation: (-8 - y) * y = -65.
Solve this quadratic equation for y: -y^2 - 8y + 65 = 0.
Use the quadratic formula to find the values of y: y = (-(-8) +/- sqrt((-8)^2 - 4 * (-1) * 65)) / (2 * (-1)).
This gives us two possible values for y: -13 and 5.
Substitute these values back into one of the original equations to find the corresponding values of x. For example, when y = -13, we have x = -8 - (-13) = 5. When y = 5, we have x = -8 - 5 = -13.
So, the two numbers that multiply to -65 and add to -8 are -13 and 5.