Question

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

Answer 1

Answer:

  -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.