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TheMathGirl
The only possible number I know is: 5 
Explanation: 5 multiplied by its-self is 25. Then if its added by itself which means 25 + 5 = 30. (I'll show you the whole thing.) 5x5=25  25+5=30.
I've thought for a while, and the only number I've found was 5. But I hope someone else can find the other number or maybe even you. :)
AL2006
The number . . . x

Multiplied by itself . . . x²

Multiplied by itself, then added to itself . . . x² + x

You said it's equal to 30, so            x² + x = 30  .

Subtract  30  from each side:      x² + x - 30 = 0   .

There you have a perfectly nice quadratic equation.
To solve it, you can either factor the left side, or use the quadratic equation.
Either way, the two solutions are

             x = 5
and
             x = -6 .
 

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