SOLUTION: {{{ 5x^2+18=3 }}} i dont understand the whole i thing

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Question 238277: +5x%5E2%2B18=3+
i dont understand the whole i thing
Found 2 solutions by checkley77, College Student:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
+5x%5E2%2B18=3+
5X^=3-18
5X^2=-15
X^2=-15/5
X^2=-3
X=SQRT-3
X=1.732i ANS.

Answer by College Student(505) About Me  (Show Source):
You can put this solution on YOUR website!
Ok. If we try to solve for x, this is what we would get:
5x%5E2%2B18=3
5x%5E2=3-18
5x%5E2=-15
x%5E2=-15%2F5
x%5E2=-3 ...same as... x=sqrt%28-3%29 (an imaginary answer)
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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.
.
"i" = sqrt%28-1%29
.
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
But in your problem, leave it as x=sqrt%28-3%29.
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I hope this explanation helped. :)