document.write( "Question 947657: Someone please help me with this.\r
\n" ); document.write( "\n" ); document.write( "Determine the values of the variable for which the expression is defined as a real number. (Enter your answer using interval notation.)\r
\n" ); document.write( "\n" ); document.write( "sqrt7x^2 − 58x + 16\r
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Algebra.Com's Answer #578302 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
If you mean $\"sqrt%287x%5E2-58x%2B16%29\"$ =sqrt(7x^2-58x+16),
\n" ); document.write( "you were missing some crucial parentheses.
\n" ); document.write( " $\"sqrt%287x%5E2-58x%2B16%29\"$ is a real number when $\"7x%5E2-58x%2B16%3E=0\"$ .
\n" ); document.write( "Otherwise, for example for $\"x=1\"$ ,
\n" ); document.write( "what's inside the square root is negative,
\n" ); document.write( "and the square root is not defined as a real number.
\n" ); document.write( "
\n" ); document.write( " $\"y=7x%5E2-58x%2B16\"$ is a quadratic function that graphs as a parabola.
\n" ); document.write( "You can try to find its zeros by using the quadratic formula.
\n" ); document.write( "It does have zeros, and they are rational numbers,
\n" ); document.write( "so factoring also works in this case.
\n" ); document.write( " $\"7x%5E2-58x%2B16=%287x-2%29%28x-8%29\"$ is zero at $\"x=2%2F7\"$ and at $\"x=8\"$ .
\n" ); document.write( "In between those numbers, $\"7x-2%3E0\"$ and $\"x-8%3C0\"$ ,
\n" ); document.write( "so their product, $\"7x%5E2-58x%2B16=%287x-2%29%28x-8%29\"$ , is negative,
\n" ); document.write( "and $\"sqrt%287x%5E2-58x%2B16%29\"$ is not defined as a real number.
\n" ); document.write( "For any other value of $\"x\"$ ,
\n" ); document.write( " $\"7x%5E2-58x%2B16=%287x-2%29%28x-8%29%3E=0\"$ ,
\n" ); document.write( "and $\"sqrt%287x%5E2-58x%2B16%29\"$ is defined as a real number.
\n" ); document.write( "So the answer is $\"%22%28%22\"$ $\"-infinity\"$ $\"%22%2C%22\"$ $\"2%2F7\"$ $\"%22%5D+U+%5B%22\"$ $\"8\"$ $\"%22%2C%22\"$ $\"infinity\"$ $\"%22%29%22\"$ . \n" ); document.write( "

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