document.write( "Question 102954: (3x-2)^2-9(3x-2)+18=0 Find real solutions of the equation. \n" ); document.write( "

Algebra.Com's Answer #74872 by Fombitz(32388) $\"\"$ $\"About$

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$\"%283x-2%29%5E2-9%283x-2%29%2B18=0\"$
\n" ); document.write( "Let $\"Y=3x-2\"$
\n" ); document.write( " $\"%283x-2%29%5E2-9%283x-2%29%2B18=0\"$
\n" ); document.write( " $\"%28Y%29%5E2-9%28Y%29%2B18=0\"$ Substitute.
\n" ); document.write( "Factoring this equation,
\n" ); document.write( " $\"%28Y-3%29%2A%28Y-6%29=0\"$ Factor the quadratic equation.
\n" ); document.write( "The solutions are Y=3 and Y=6, but you need answers in x.
\n" ); document.write( "For Y=3,
\n" ); document.write( " $\"Y=3x-2=3\"$
\n" ); document.write( " $\"3x-2%2B2=3%2B2\"$
\n" ); document.write( " $\"3x=5\"$
\n" ); document.write( " $\"x=5%2F3\"$
\n" ); document.write( "For Y=6,
\n" ); document.write( " $\"Y=3x-2=6\"$
\n" ); document.write( " $\"3x-2%2B2=6%2B2\"$
\n" ); document.write( " $\"3x=8\"$
\n" ); document.write( " $\"x=8%2F3\"$
\n" ); document.write( "Two solutions : $\"x+=+5%2F3\"$ and $\"x=8%2F3\"$
\n" ); document.write( "The substitution helps out by simplifying the multiplication and factoring.
\n" ); document.write( "Let's verify one solution:
\n" ); document.write( " $\"%283x-2%29%5E2-9%283x-2%29%2B18=0\"$
\n" ); document.write( " $\"%283%2A5%2F3-2%29%5E2-9%283%2A5%2F3-2%29%2B18=0\"$
\n" ); document.write( " $\"9-27%2B18=0\"$
\n" ); document.write( " $\"0=0\"$
\n" ); document.write( "True, Good answer. \n" ); document.write( "

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