What adds up to 7 and can also be multiplied to -30

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Abocc Abocc

22-02-2016
Mathematics

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What adds up to 7 and can also be multiplied to -30

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Panoyin Panoyin · Answer 1 · 2016-02-22T23:38:15+01:00

x + y = 7
xy = -30

x + y = 7
x - x + y = -x + 7
y = -x + 7

  xy = -30
x(-x + 7) = -30
x(-x) + x(7) = 30
-x² + 7x = -30
-x² + 7x + 30 = 0
-1(x²) - 1(-7x) - 1(-30) = 0
  -1(x² - 7x - 30) = 0
-1 -1
  x² - 7x - 30 = 0
  x² - 10x + 3x - 30 = 0
x(x) - x(10) + 3(x) - 3(10) = 0
  x(x - 10) + 3(x - 10) = 0
(x + 3)(x - 10) = 0
  x + 3 = 0 or x - 10 = 0
- 3 - 3 + 10 + 10
x = -3    or    x = 10

x + y = 7    or   x + y = 7
  -3 + y = 7 or 10 + y = 7
+ 3 + 3 - 10 - 10
y = 10     or y = -3
(x, y) = (-3, 10) or (x, y) = (10, -3)

The two numbers that add up to 7 and multiply to 30 are -3 and 10.