document.write( "Question 238277: $\"+5x%5E2%2B18=3+\"$
\n" ); document.write( "i dont understand the whole i thing \n" ); document.write( "

Algebra.Com's Answer #175105 by College Student(505) $\"\"$ $\"About$

You can put this solution on YOUR website!
Ok. If we try to solve for x, this is what we would get:
\n" ); document.write( " $\"5x%5E2%2B18=3\"$
\n" ); document.write( " $\"5x%5E2=3-18\"$
\n" ); document.write( " $\"5x%5E2=-15\"$
\n" ); document.write( " $\"x%5E2=-15%2F5\"$
\n" ); document.write( " $\"x%5E2=-3\"$ ...same as... $\"x=sqrt%28-3%29\"$ (an imaginary answer)
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\n" ); document.write( "Now, we know that if we multiply two negative numbers, the result will always be a positive number. But in this problem, we see that a number raised to the second power (same as having a number multiplied by itself) should equal -3. This directly contradicts the rule. So, Rafael Bombelli (back in 1572) invented the imaginary number we know as \"i\" to be able to work out these problems.
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\n" ); document.write( "\"i\" = $\"sqrt%28-1%29\"$
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\n" ); document.write( "Suppose the answer would have been $\"x=sqrt%28-9%29\"$ ... since we know the square root of 9 is 3, we could then say $\"x=3sqrt%28-1%29\"$ ...same as... $\"x=3i\"$
\n" ); document.write( "But in your problem, leave it as $\"x=sqrt%28-3%29\"$ .
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\n" ); document.write( "I hope this explanation helped. :) \n" ); document.write( "

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