document.write( "Question 75666: can i please get help with this? \r
\n" ); document.write( "\n" ); document.write( "x^2-10x+24=0 \n" ); document.write( "
Algebra.Com's Answer #54353 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"x%5E2-10x%2B24=0\"
\n" ); document.write( "List the possible numbers that multiply to 24:
\n" ); document.write( "1,2,3,4,6,8,12,24
\n" ); document.write( "And you could also have negative numbers since (-8)(-3)=24. So of these possible factors, which 2 numbers add to -10? Lets look at (-8) and (-3), they multiply to 24 but add to -11, so that doesn't work. Lets look at (-12) and (-2): they add to -14, that doesn't work either. Finally lets look at (-6) and (-4): they add to -10 and that works. In practice this might take longer since I already knew the answer but just wanted to show the process. So the polynomial \"x%5E2-10x%2B24=0\" factors to
\n" ); document.write( "\"%28x-6%29%28x-4%29=0\" which if foiled becomes \"x%5E2-10x%2B24=0\" again. So now set each factor equal to zero individually. The reason why this works is because we can say
\n" ); document.write( "\"pq=0\"
\n" ); document.write( "\"p=0\" divide both sides by q
\n" ); document.write( "and
\n" ); document.write( "\"q=0\" divide both sides by p. So if either p or q is 0 (or both) then the entire equation equals zero.
\n" ); document.write( "The same applies to \"%28x-6%29%28x-4%29=0\"
\n" ); document.write( "\"%28%28x-6%29%2Across%28x-4%29%29%2F%28cross%28x-4%29%29=0%2F%28x-4%29\" divide both sides by (x-4)
\n" ); document.write( "\"x-6=0\"
\n" ); document.write( "\"x%2Bcross%28-6%2B6%29=0%2B6\" Add 6 to both sides
\n" ); document.write( "\"x=6\"
\n" ); document.write( "\"%28cross%28x-6%29%2A%28x-4%29%29%2F%28cross%28x-6%29%29=0%2F%28x-6%29\" divide both sides by (x-6)
\n" ); document.write( "\"x-4=0\"
\n" ); document.write( "\"x%2Bcross%28-4%2B4%29=0%2B4\" Add 4 to both sides
\n" ); document.write( "\"x=4\"
\n" ); document.write( "So the answers are x=6 or x=4\r
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\n" ); document.write( "\n" ); document.write( "Or you could always plug the coefficients into the quadratic formula:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-10x%2B24+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-10%29%5E2-4%2A1%2A24=4\".
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\n" ); document.write( " Discriminant d=4 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--10%2B-sqrt%28+4+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+6\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-10%29-sqrt%28+4+%29%29%2F2%5C1+=+4\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-10x%2B24\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-10x%2B24+=+1%28x-6%29%2A%28x-4%29\"
\n" ); document.write( " Again, the answer is: 6, 4.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B24+%29\"
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