document.write( "Question 821367: x^3+10x=80
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Algebra.Com's Answer #494606 by tommyt3rd(5050) $\"\"$ $\"About$

You can put this solution on YOUR website!
Assuming you want an approximate real solution we can use Newton's method. Writing f(x)=x^3+10x-80, and f'(x)=3x^2+10 and writing as a sequence we can see:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5Bn%2B1%5D=x%5Bn%5D-%28x%5Bn%5D%5E3%2B10x%5Bn%5D-80%29%2F%283x%5Bn%5D%5E2%2B10%29\"$ \r
\n" ); document.write( "\n" ); document.write( "For a reasonable first guess we can use the fact that when x=3, the LHS of the original equation is 57 and when x=4, LHS=104. So let's split the difference and choose x=3.5\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5B2%5D=3.545454\"$
\n" ); document.write( " $\"x%5B3%5D=3.54499\"$
\n" ); document.write( " $\"x%5B4%5D=3.54499\"$ \r
\n" ); document.write( "\n" ); document.write( "so probably close enough...\r
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