document.write( "Question 755056: How do you find out if an equation has real numbers? For example, x^2-9=0, x^2+7=1, 3x-7=14, which one has no real solutions? \n" ); document.write( "

Algebra.Com's Answer #459483 by josmiceli(19441) $\"\"$ $\"About$

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If there is a $\"+sqrt%28-1%29+\"$ in the solutions, then
\n" ); document.write( "the solutions are not all real.
\n" ); document.write( "(a)
\n" ); document.write( " $\"+x%5E2+-+9+=+0+\"$
\n" ); document.write( "Add $\"9\"$ to both sides
\n" ); document.write( " $\"+x%5E2+=+9+\"$
\n" ); document.write( " $\"+x+=+3+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+x+=+-3+\"$
\n" ); document.write( "Both are real solutions
\n" ); document.write( "-------------------
\n" ); document.write( "(b)
\n" ); document.write( " $\"+x%5E2+%2B+7+=+1+\"$
\n" ); document.write( "Subtract $\"+7+\"$ from both sides
\n" ); document.write( " $\"+x%5E2+=+-6+\"$
\n" ); document.write( " $\"+x+=+sqrt%28-1%29%2Asqrt%286%29+\"$
\n" ); document.write( " $\"+x+=+sqrt%286%29%2Ai+\"$
\n" ); document.write( "and also,
\n" ); document.write( " $\"+x+=+-%28+sqrt%28-1%29%2Asqrt%286%29+%29+\"$
\n" ); document.write( " $\"+x+=+-sqrt%286%29%2Ai+\"$
\n" ); document.write( "There are no real solutions
\n" ); document.write( "-----------------------
\n" ); document.write( "(c)
\n" ); document.write( " $\"+3x+-+7+=+14+\"$
\n" ); document.write( " $\"+3x+=+21+\"$
\n" ); document.write( " $\"+x+=+7+\"$
\n" ); document.write( "There is 1 real solution\r
\n" ); document.write( "
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