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What adds to 7 and multiplies to -30

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x, y - the numbers

The numbers add up to 7.
[tex]x+y=7 \\ y=7-x[/tex]

The numbers multiply to -30.
[tex]xy=-30 \\ \hbox{substitute 7-x for y:} \\ x(7-x)=-30 \\ 7x-x^2=-30 \\ -x^2+7x+30=0 \\ -x^2-3x+10x+30=0 \\ -x(x+3)+10(x+3)=0 \\ (-x+10)(x+3)=0 \\ -x+10=0 \ \lor \ x+3=0 \\ x=10 \ \lor \ x=-3 \\ \\ y=7-x \\ y=7-10 \ \lor \ y=7-(-3) \\ y=-3 \ \lor \ y=10 \\ \\ (x,y)=(10,-3) \ or \ (-3,10)[/tex]

-3 and 10 add up to 7 and multiply to -30.
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