document.write( "Question 396535: 27X^2/25 = 1/3 \n" ); document.write( "

Algebra.Com's Answer #281292 by jsmallt9(3758) $\"\"$ $\"About$

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$\"27X%5E2%2F25+=+1%2F3\"$
\n" ); document.write( "First let's eliminate the fraction by multiplying both sides by 25:
\n" ); document.write( " $\"27X%5E2+=+25%2F3\"$
\n" ); document.write( "Dividing both sides by 27 isolates the base, x, and its exponent, 2:
\n" ); document.write( " $\"X%5E2+=+25%2F81\"$
\n" ); document.write( "Now we can find the square root of each side:
\n" ); document.write( " $\"sqrt%28X%5E2%29+=+sqrt%2825%2F81%29\"$
\n" ); document.write( "On the left side we get not \"x\" but $\"abs%28x%29\"$ . This is so because a square root is supposed to be positive but we do not know if x is positive. Using absolute value like this ensures that we get a positive square root.
\n" ); document.write( " $\"abs%28X%29+=+sqrt%2825%2F81%29\"$
\n" ); document.write( "On the right side we can use a property of radicals, $\"root%28a%2C+p%29%2Froot%28a%2C+q%29+=+root%28a%2C+p%2Fq%29\"$ , to split the square root of a fraction into a fraction of the square roots of the numerator and denominator:
\n" ); document.write( " $\"abs%28X%29+=+sqrt%2825%29%2Fsqrt%2881%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"abs%28x%29+=+5%2F9\"$
\n" ); document.write( "Solving the absolute value equation we get:
\n" ); document.write( " $\"x+=+5%2F9\"$ or $\"x+=+%28-5%29%2F9\"$
\n" ); document.write( "These are both solutions to your equation. \n" ); document.write( "

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