document.write( "Question 59749: Determine the solution or solutions of each equation\r
\n" ); document.write( "\n" ); document.write( "\"++2%5Ex%5E2=32%282%5E%284x%29%29++\" \n" ); document.write( "
Algebra.Com's Answer #40990 by uma(370)\"\" \"About 
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2^(x^2) = 32(2^4x)
\n" ); document.write( "==> 2^(x^2) = (2^5)(2^4x) [32 = 2^5]
\n" ); document.write( "==> 2^(x^2) = 2^(5+4x) [law of exponents: x^a * x^b = x^(a+b)]
\n" ); document.write( "AS the bases are the same on both the sides, the exponents can be equated.
\n" ); document.write( "==> x^2 = 5+4x
\n" ); document.write( "==> x^2-4x = 5 [subtracting 4x from both the sides]
\n" ); document.write( "==>x^2 - 4x - 5 = 0 [subtracting 5 from either side]
\n" ); document.write( "==>x^2 + x - 5x - 5= 0 [splitting the middle term]
\n" ); document.write( "==>x(x+1) - 5(x+1) = 0 [taking the common factor out]
\n" ); document.write( "==>(x + 1)(x - 5) = 0
\n" ); document.write( "==> x + 1 = 0 or x - 5 = 0
\n" ); document.write( "==> x = -1 or x = 5\r
\n" ); document.write( "\n" ); document.write( "Ans: x = -1, 5\r
\n" ); document.write( "\n" ); document.write( "Good Luck!!!
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