Find all value of x where 5 - x^2 < 8

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The inequality 5 - x^2 < 8 simplifies to x^2 > -3. Since the square of any real number is always non-negative, this inequality holds true for all real numbers. Therefore, the solution set for the inequality is all real numbers. It is important to remember that if an equation results in x^2 being greater than a negative number, the inequality is satisfied by all real numbers. The conclusion confirms that x can take any real value.
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Homework Statement



Find all value of x where 5 - x^2 < 8

Homework Equations





The Attempt at a Solution



-x^2 &lt; 3 \Rightarrow x^2 &gt; -3 \Rightarrow x &gt; \sqrt{-3}

But I can't square root a negative number?
 
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zeion said:

Homework Statement



Find all value of x where 5 - x^2 < 8

Homework Equations





The Attempt at a Solution



-x^2 &lt; 3 \Rightarrow x^2 &gt; -3 \Rightarrow x &gt; \sqrt{-3}

But I can't square root a negative number?
x2 > -3 for all real numbers.
 
Mark44 said:
x2 > -3 for all real numbers.

So does that mean x is the set of all real numbers? Because any real number squared is positive.
 
Yes, the solution set is all real numbers. Something to remember: If you ever get an equation where x2 > some negative number, the inequality is true for all real numbers.
 

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