factor 4 4=1 times 4 2 times 2 they don't add to 2 set up equation x+y=2 xy=4 first equation, subtract x from both sides y=2-x subsitute for y x(2-x)=4 distribute 2x-x^2=4 add x^2 2x=x^2+4 subtract 2x 0=x^2-2x+4 use quadratic formula which is if you have ax^2+bx+c=0 then x=[latex] \frac{ -b+/-\sqrt{b^{2}-4ac} }{2a} [/latex] so 1x^2-2x+4=0 a=1 b=-2 c=4 x=[latex] \frac{ -(-2)+/-\sqrt{(-2)^{2}-4(1)(4)} }{2(1)} [/latex] x=[latex] \frac{ 2+/-\sqrt{4-16} }{2} [/latex] x=[latex] \frac{ 2+/-\sqrt{-12} }{2} [/latex] we have [latex] \sqrt{-12} [/latex] and that doesn't give a real solution therefor there are no real solutions but if you want to solve fully x=[latex] \frac{ 2+/-2\sqrt{-3} }{2} [/latex] i=[latex] \sqrt{-1} [/latex] x=[latex] \frac{ 2+/-2i\sqrt{3} }{2} [/latex] x=[latex] 1+/-i\sqrt{3} [/latex] x=[latex] 1-i\sqrt{3} [/latex] or x=[latex] 1+i\sqrt{3} [/latex] (those are the 2 numbers)

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