x + y = -30
xy = 62
x + y = -30
- x - x
y = -x - 30
xy = 62
x(-x - 30) = 62
x(-x) - x(30) = 62
-x² - 30x = 62
- 62 - 62
-x² - 30x - 62 = 0
-1(x²) - 1(30x) - 1(62) = 0
-1(x² + 30x + 62) = 0
-1 -1
x² + 30x + 62 = 0
x = -(30) ± √((30)² - 4(1)(62))
2(1)
x = -30 ± √(900 - 248)
2
x = -30 ± √(652)
2
x = -30 ± 2√(163)
2
x = -15 ± √(163)
x = -15 ± 12.76
x = -15 + 12.76 or x = -15 - 12.76
x = -2.24 or x = -27.76
x + y = -30 or x + y = -30
-2.24 + y = -30 or -27.76 + y = -30
+ 2.24 + 2.24 + 27.76 + 27.76
y = -27.76 or y = -2.24
(x, y) = (-2.24, -27.76) or (x, y) = (-27.76, -2.24)
The two numbers that add up to -30 and multiply to 72 are -2.24 and -27.76.
