What two numbers multiply to -8 and add to -4

The two numbers are -5.4641, and 1.4641.

Let x and y be two numbers.

Then according to question product of these numbers is -8 and sum is -4

That is

and

From (2) we get

Substituting in (1), we get  

Simplifying these we get two numbers x=-5.4641, 1.4641

and y = -4 + 5.4641 = 1.4641,

y=-4 - 1.4641=-5.4641

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  -2-2√3, -2+2√3

Step-by-step explanation:

Let x represent one of the numbers. Then the other number is -4-x. We want the product to be -8:

  x(-4-x) = -8

  -4x -x^2 = -8 . . . . . eliminate parentheses

  x^2 +4x = 8 . . . . . . multiply by -1

  x^2 +4x +4 = 12 . . . add 4 to complete the square

  (x +2)^2 = 12

  x +2 = ±√12 = ±2√3

  x = -2±2√3

The two numbers are -2-2√3 ≈ -5.4641, and -2+2√3 ≈ 1.4641.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

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