markp4checo
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# What two numbers multiply to 54 and add up to 7

xy = 54 x + y = 7 $xy = 54$ $\frac{xy}{x} = \frac{54}{x}$ $y = \frac{54}{x}$ $x + y = 7$ $x + \frac{54}{x} = 7$ $\frac{x^{2}}{x} + \frac{54}{x} = 7$ $\frac{x^{2} + 54}{x} = 7$ $x^{2} + 54 = 7x$ $x^{2} - 7x + 54 = 0$ $x = \frac{-(-7) \± \sqrt{(-7)^{2} - 4(1)(54)}}{2(1)}$ $x = \frac{7 \± \sqrt{49 - 216}}{2}$ $x = \frac{7 \± \sqrt{-167}}{2}$ $x = \frac{7 \± i\sqrt{167}}{2}$ $x = \frac{7 \± 12.9i}{2}$ $x = 3.5 \± 6.45i$ $x = 3.5 + 6.45i$    $or$    ﻿﻿$3.5 - 6.45i$                   x + y = 7    3.5 + 6.45i + y = 7 - (3.5 + 6.45i)       - (3.5 + 6.45i)                         y = 3.5 - 6.45i                   (x, y) = (3.5 + 6.45i, (3.5 - 6.45i)                           or                   x + y = 7    3.5 - 6.45i + y = 7 - (3.5 - 6.45i)     - (3.5 - 6.45i)                        y = 3.5 + 6.45i                  (x, y) = (3.5 - 6.45i, 3.5 + 6.45i) The two numbers that add up to 7 and can multiply to 54 is 3.5 ± 6.45i.