document.write( "Question 710844: 16v^2-25=0 \n" ); document.write( "

Algebra.Com's Answer #437286 by jsmallt9(3758) $\"\"$ $\"About$

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$\"16v%5E2-25=0\"$
\n" ); document.write( "Equations with whole number exponents greater than 1, like this one, are often solved by making one side of the equation zero, factoring the other side and then using the Zero Product Property.

\n" ); document.write( "Our equation already has one side that is zero. So we proceed to the factoring. Fortunately the left side is a difference of squares. $\"16v%5E2+=+%284v%29%5E2\"$ and $\"25+=+%285%29%5E2\"$ . So we can use the difference of squares pattern, $\"a%5E2+-+b%5E2+=+%28a%2Bb%29%28a-b%29\"$ , to factor the left side (with the \"a\" being \"4v\" and the \"b\" being \"5\"):
\n" ); document.write( " $\"%284v%2B5%29%284v-5%29+=+0\"$
\n" ); document.write( "From the Zero Product Property we know that a product can be zero only if one (or more) of the factors is zero. So:
\n" ); document.write( " $\"4v%2B5+=+0\"$ or $\"4v-5+=+0\"$
\n" ); document.write( "Solving these we should get:
\n" ); document.write( " $\"v+=+-5%2F4\"$ or $\"v+=+5%2F4\"$
\n" ); document.write( "These are the solution to the equation. \n" ); document.write( "

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