Question

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

Answer 1

9514 1404 393

Answer:

8 ± √34 ≈ {2.169, 13.831}

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}