What two numbers multiple to get -12 and add to -5

Original question: What two numbers multiply to get -12 and add to -5.

Pairs of numbers (1.772, -6.772) and (-6.772, 1.772).

Step-by-step explanation:

Let and be the two numbers, the we know that

(1).

and

(2).

We solve for in equation(2) and substitute this into equation(1)

This is a quadratic equation, and its solutions are

we substitute these two solutions into equation(1) and find the corresponding values:

Thus we have two pairs of numbers which multiply to give -12 and add to give -5

and

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: