Question

What adds up to -7 but multiplies to 10

Answer 1

x + y = -7
xy = 10

$xy = -7$
$\frac{xy}{x} = \frac{-7}{x}$
$y = \frac{-7}{x}$

$x + y = -7$
$x + \frac{-7}{x} = -7$
$\frac{x^{2}}{x} + \frac{-7}{x} = 7$
$\frac{x^{2} - 7}{x} = -7$
$x^{2} - 7 = -7x$
$x^{2} + 7x - 7 = 0$
$x = \frac{-(7) \± \sqrt{(7)^{2} - 4(1)(-7)}}{2(1)}$
$x = \frac{-7 \± \sqrt{49 + 28}}{2}$
$x = \frac{-7 \± \sqrt{77}}{2}$
$x = \frac{-7 \± 8.8}{2}$
$x = \frac{-7 + 8.8}{2}$    $or$    $x = \frac{-7 - 8.8}{2}$
$x = \frac{1.8}{2}$    $or$    $x = \frac{-15.8}{2}$
$x = 0.9$    $or$    $x = -7.9$

     x + y = -7
  0.9 + y = -7
- 0.9      - 0.9
           y = -7.9
     (x, y) = (0.9, -7.9)

              or

      x + y = -7
  -7.9 + y = -7
+ 7.9        + 7.9
            y = 0.9
      (x, y) = (-7.9, 0.9)

The two numbers that add up to -7 and multiply to -10 are -7.9 and 0.9.