document.write( "Question 549311: h=-9.8t^2+15t+160 \n" ); document.write( "

Algebra.Com's Answer #357616 by JBarnum(2146) $\"\"$ $\"About$

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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"at%5E2%2Bbt%2Bc=0\"$ (in our case $\"-9.8t%5E2%2B15t%2B160+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%2815%29%5E2-4%2A-9.8%2A160=6497\"$ .
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\n" ); document.write( " Discriminant d=6497 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28-15%2B-sqrt%28+6497+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"t%5B1%5D+=+%28-%2815%29%2Bsqrt%28+6497+%29%29%2F2%5C-9.8+=+-3.34714133293605\"$
\n" ); document.write( " $\"t%5B2%5D+=+%28-%2815%29-sqrt%28+6497+%29%29%2F2%5C-9.8+=+4.87775357783401\"$
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\n" ); document.write( " Quadratic expression $\"-9.8t%5E2%2B15t%2B160\"$ can be factored:
\n" ); document.write( " $\"-9.8t%5E2%2B15t%2B160+=+-9.8%28t--3.34714133293605%29%2A%28t-4.87775357783401%29\"$
\n" ); document.write( " Again, the answer is: -3.34714133293605, 4.87775357783401.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-9.8%2Ax%5E2%2B15%2Ax%2B160+%29\"$

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