What two numbers multiply together to equal 180 and add together to equal 8?

Answer 1

Solving using algebra:

Let's call the two numbers x and y. We know that xy = 180 and that x + y = 8. We can use the second equation to say that y = 8 - x, and plug that into the first equation for y to get: x(8-x) = 180Distribute:

8x - x2 = 180

-x2 + 8x = 180

x2 - 8x = -180This can be solved using the quadratic formula or by completing the square. Here is completing the square:

x2 - 8x + 16 = -180 + 16

(x-4)2 = -164

x - 4 = ±√(-164)Since this involves taking the square root of a negative number, the numbers x and y are imaginary. If you are not concerned with imaginary numbers, then there are no numbers that multiply to 180 and add to 8.

If you are concerned with imaginary numbers, you can continue solving the equation:

x = 4 ±√(-164)

x = 4 ±i√(164)

x = 4 ± 2i√(41)

So the two numbers are 4 + 2i√(41) and 4 - 2i√(41).