What two numbers can be added to get a sum of 16, and multiplied to get a product of 30?

9514 1404 393

  8 ± √34 ≈ {2.169, 13.831}

Step-by-step explanation:

Let x represent one of the numbers. Then the other is 16 -x and their product is ...

  x(16 -x) = 30

  x^2 -16x = -30 . . . . . eliminate parentheses, multiply by -1

  x^2 -16x +64 = 34 . . . . add 64 to complete the square

  (x -8)^2 = 34 . . . . . . . . rewrite

  x -8 = ±√34 . . . . . . . .square root

  x = 8 ± √34 . . . . . . add 8

  x ≈ {2.169, 13.831}

11 feet 6 inches and 8 feet 6 inches

47 - 90 = 43

43 - 180 = x

x = 137