document.write( "Question 61958This question is from textbook
\n" ); document.write( ": Solve the equation.
\n" ); document.write( "cuberoot2^(2-x) = 2^(x^2)
\n" ); document.write( "This problem is very confusing for me, please help! \n" ); document.write( "
Algebra.Com's Answer #42700 by funmath(2933)\"\" \"About 
You can put this solution on YOUR website!
Solve the equation.
\n" ); document.write( "cuberoot2^(2-x) = 2^(x^2)
\n" ); document.write( "\"%282%5E%282-x%29%29%5E%281%2F3%29=2%5E%28x%5E2%29\"
\n" ); document.write( "\"2%5E%28%281%2F3%29%282-x%29%29=2%5E%28x%5E2%29\" Since the bases are the same, their exponents are equal.
\n" ); document.write( "\"%281%2F3%29%282-x%29=x%5E2\"
\n" ); document.write( "\"3%281%2F3%29%282-x%29=3x%5E2\"
\n" ); document.write( "\"2-x=3x%5E2\"
\n" ); document.write( "\"2-2-x%2Bx=3x%5E2%2Bx-2\"
\n" ); document.write( "\"0=3x%5E2%2Bx-2\" Factor by what ever method you use, I'm using arch,ac,or grouping.
\n" ); document.write( "\"0=3x%5E2%2B3x-2x-2\"
\n" ); document.write( "\"0=%283x%5E2%2B3x%29%2B%28-2x-2%29\"
\n" ); document.write( "\"0=3x%28x%2B1%29-2%28x%2B1%29\"
\n" ); document.write( "\"0=%28x%2B1%29%283x-2%29\" Set each parntheses=0.
\n" ); document.write( "x+1=0 and 3x-2=0
\n" ); document.write( "x+1-1=0-1 and 3x-2+2=0+2
\n" ); document.write( "x=-1 and 3x=2
\n" ); document.write( "x=-1 and 3x/3=2/3
\n" ); document.write( "x=-1 and x=2/3
\n" ); document.write( ":
\n" ); document.write( "Check:
\n" ); document.write( "for x=-1
\n" ); document.write( "cubedroot \"2%5E%282-%28-1%29%29=2%5E%28%28-1%29%5E2%29\"
\n" ); document.write( "cubed root \"2%5E%282%2B1%29=2%5E1\"
\n" ); document.write( "cubed root \"2%5E3=2\"
\n" ); document.write( "\"2=2\" x=-1 is valid
\n" ); document.write( "for x=2/3
\n" ); document.write( "cubed root \"2%5E%282-%282%2F3%29%29=2%5E%28%282%2F3%29%5E2%29\"
\n" ); document.write( "cubed root \"2%5E%286%2F3-2%2F3%29=2%5E%284%2F9%29\"
\n" ); document.write( "cubed root \"2%5E%284%2F3%29=2%5E%284%2F9%29\"
\n" ); document.write( "\"2%5E%284%2F9%29=2%5E%284%2F9%29\" x=2/3 is also valid.
\n" ); document.write( "There's another method for solving this, but you have to use a calculator if you take the log of both sides, so don't freak out if this is not the method you were taught.
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "
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