document.write( "Question 276813: needing help with finding what x equals in this equation\r
\n" ); document.write( "\n" ); document.write( "4(2x-7)^5=12 \n" ); document.write( "

Algebra.Com's Answer #201852 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
To solve for x means to transform the equation so that it has the form
\n" ); document.write( "x = something
\n" ); document.write( "or
\n" ); document.write( "something = x

\n" ); document.write( "With your equation, to get the x by itself on one side of the equation, we will need to get rid of the 4, the 2 the -7 and the 5 (not in that order). To get rid of all these we need to \"peel away\" from the outside. So we start by getting rid of the 4 which is separate from the expression in parentheses and its exponent. We can divide both sides by 4 giving:
\n" ); document.write( " $\"%282x-7%29%5E5=3\"$
\n" ); document.write( "Still peeling away from the out side, the 5 is the next to go. We can find the 5th root of each side:
\n" ); document.write( " $\"root%285%2C+%282x-7%29%5E5%29+=+root%285%2C+3%29\"$
\n" ); document.write( "The left side simplifies to:
\n" ); document.write( " $\"2x-7+=+root%285%2C+3%29\"$
\n" ); document.write( "The next to go is the -7 (since it is separate from the term with x in it). We can just add 7 to each side:
\n" ); document.write( " $\"2x+=+7+%2B+root%285%2C+3%29\"$
\n" ); document.write( "(I put the 7 in front on the right side so that it cannot be thought of as part of the 5th root.) The 2 is the last to go. Divide both sides by 2:
\n" ); document.write( " $\"x+=+%287+%2B+root%285%2C+3%29%29%2F2\"$
\n" ); document.write( "which is the answer to the problem. (If you need a decimal approximation then use your calculator on the right side. To find a 5th root with your calculator, just raise 3 to the 0.2 power (since 5th roots are exponents of 1/5 and 1/5 as a decimal is 0.2).) \n" ); document.write( "

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