document.write( "Question 185416This question is from textbook prentice hall mathematics algebra 2
\n" ); document.write( ": please help me with these two problems\r
\n" ); document.write( "\n" ); document.write( "\"x%5E3%2B64=0\"
\n" ); document.write( "this is how far i got
\n" ); document.write( "x^3+64=x+21.3
\n" ); document.write( "=(x+21.3)((x^2)-x+21.3)
\n" ); document.write( "=(x+21.3)(x^2-x+21.3)\r
\n" ); document.write( "\n" ); document.write( "and i have one more problem\r
\n" ); document.write( "\n" ); document.write( "\"x%5E3-125=0\" \n" ); document.write( "
Algebra.Com's Answer #139111 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
1) Solve:
\n" ); document.write( "\"x%5E3%2B64+=+0\" This is the sum of two cubes: \"%28x%29%5E3%2B%284%29%5E3\" and this is factorable as:
\n" ); document.write( "\"A%5E3%2BB%5E3+=+%28A%2BB%29%28A%5E2-AB%2BB%5E2%29\" and in your problem, A = x and B = 4,so...
\n" ); document.write( "\"x%5E3%2B64+=+%28x%2B4%29%28x%5E2-4x%2B16%29\", so...
\n" ); document.write( "\"%28x%2B4%29%28x%5E2-4x%2B16%29+=+0\" Applying the zero product rule, we get:
\n" ); document.write( "\"x%2B4+=+0\" or \"x%5E2-4x%2B16++=0\"
\n" ); document.write( "If \"x%2B4+=+0\" then \"highlight%28x+=+-4%29\" and...
\n" ); document.write( "If \"x%5E2-4x%2B16+=+0\" Use the quadratic formula (\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\") to solve:
\n" ); document.write( "\"x+=+%28-%28-4%29%2B-sqrt%28%28-4%29%5E2-4%281%29%2816%29%29%29%2F2%281%29\"
\n" ); document.write( "\"x+=+%284%2B-sqrt%2816-64%29%29%2F2\"
\n" ); document.write( "\"x+=+%284%2B-sqrt%28-48%29%29%2F2\" Simplifying this, we get:
\n" ); document.write( "\"x+=+%284%2B-sqrt%2816%2A%28-3%29%29%29%2F2\"
\n" ); document.write( "\"x+=+2%2B2%2Asqrt%28-3%29\" or \"x+=+2-2sqrt%28-3%29\" or these can be written in terms of \"i+=+sqrt%28-1%29\"
\n" ); document.write( "\"highlight%28x+=+2%2B2sqrt%283%29i%29\"} or \"highlight%28x+=+2-2sqrt%283%29i%29\"
\n" ); document.write( "So the three roots (there are three because it's a cubic equation) are:
\n" ); document.write( "\"highlight%28x+=+-4%29\"
\n" ); document.write( "\"highlight%28x+=+2%2B2sqrt%283%29i%29\"
\n" ); document.write( "\"highlight%28x+=+2-2sqrt%283%29i%29\"
\n" ); document.write( "-------------------------------------------------------------------
\n" ); document.write( "2) Solve:
\n" ); document.write( "\"x%5E3-125+=+0\" This is the difference of two cubes (\"%28x%29%5E3-%285%29%5E3\") and this is factorable as: \"A%5E3-B%5E3+=+%28A-B%29%28A%5E2%2BAB%2BB%5E2%29\" and in this problem, A = x and B = 5, so...
\n" ); document.write( "\"x%5E3-125+=+%28x-5%29%28x%5E2%2B5x%2B25%29\" so...
\n" ); document.write( "\"%28x-5%29%28x%5E2%2B5x%2B25%29+=+0\" Again, applying the zero product rule, we get:
\n" ); document.write( "\"x-5+=+0\" or \"x%5E2%2B5%2B25+=+0\" so...
\n" ); document.write( "If \"x-5+=+0\" then \"highlight%28x+=+5%29\" or
\n" ); document.write( "If \"x%5E2%2B5x%2B25+=+0\" Use the quadratic formula to solve:
\n" ); document.write( "\"x+=+%28-5%2B-sqrt%285%5E2-4%281%29%2825%29%29%29%2F2%281%29\" Simplifying, we get:
\n" ); document.write( "\"x+=+%28-5%2B-sqrt%28-75%29%29%2F2\"
\n" ); document.write( "\"x+=+%28-5%2B-sqrt%2825%2A%28-3%29%29%29%2F2\"
\n" ); document.write( "\"x+=+%28-5%2F2%29%2B%285%2F2%29sqrt%28-3%29\" or \"x+=+%28-5%2F2%29-%285%2F2%29sqrt%28-3%29%29\" which can be written as:
\n" ); document.write( "\"highlight%28x+=+%28-5%2F2%29%281-sqrt%283%29i%29%29\" or \"highlight%28x+=+%28-5%2F2%29%281%2Bsqrt%283%29i%29%29\"
\n" ); document.write( "So the three roots are:
\n" ); document.write( "\"highlight%28x+=+5%29\"
\n" ); document.write( "\"highlight%28x+=+%28-5%2F2%29%281-sqrt%283%29i%29%29\"
\n" ); document.write( "\"highlight%28x+=+%28-5%2F2%29%281%2Bsqrt%283%29i%29%29\"
\n" ); document.write( " \n" ); document.write( "
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