document.write( "Question 943435: Volume= 126ft^3
\n" ); document.write( "Height = x
\n" ); document.write( "Length = x+3
\n" ); document.write( "Width = x+4\r
\n" ); document.write( "\n" ); document.write( "What is x? \n" ); document.write( "

Algebra.Com's Answer #575177 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( " $\"V=L%2AW%2Ah\"$ \r
\n" ); document.write( "\n" ); document.write( "if
\n" ); document.write( " $\"Volume=+126ft%5E3\"$
\n" ); document.write( "Height $\"h=+x\"$
\n" ); document.write( "Length $\"L=+x%2B3\"$
\n" ); document.write( "Width $\"W=+x%2B4\"$ \r
\n" ); document.write( "\n" ); document.write( "then\r
\n" ); document.write( "\n" ); document.write( " $\"126=%28x%2B3%29%2A%28x%2B4%29%2Ax\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"126=%28x%5E2%2B4x%2B3x%2B12%29%2Ax\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"126=x%5E3%2B7x%5E2%2B12x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=x%5E3%2B7x%5E2%2B12x-126\"$ ........write $\"7x%5E2\"$ as $\"-3x%5E2%2B10x%5E2\"$ and $\"12x\"$ as $\"-30x%2B42x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3-3x%5E2%2B10x%5E2-30x%2B42x-126=0\"$ ...group\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E3-3x%5E2%29%2B%2810x%5E2-30x%29%2B%2842x-126%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%28x-3%29%2B10x%28x-3%29%2B42%28x-3%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-3%29%28x%5E2%2B10x%2B42%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( "real root is:\r
\n" ); document.write( "\n" ); document.write( "if $\"%28x-3%29=0\"$ => $\"x=3\"$ \r
\n" ); document.write( "\n" ); document.write( "here $\"%28x%5E2%2B10x%2B42%29=0\"$ we have $\"a=1\"$ , $\"b=10\"$ and $\"c=42\"$ \r
\n" ); document.write( "\n" ); document.write( "since $\"c%3Eb\"$ , determinant $\"b%5E2-4ac\"$ is negative, so we will have two complex roots and we do not need them for length and width\r
\n" ); document.write( "\n" ); document.write( "so, we will use $\"x=3\"$ \r
\n" ); document.write( "\n" ); document.write( "then\r
\n" ); document.write( "\n" ); document.write( "Height $\"h=+3ft\"$
\n" ); document.write( "Length $\"L=+6ft\"$
\n" ); document.write( "Width $\"W=+7ft\"$ \r
\n" ); document.write( "\n" ); document.write( "check the volume:\r
\n" ); document.write( "\n" ); document.write( " $\"V=L%2AW%2Ah\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"V=6ft%2A7ft%2A3ft\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"V=126ft%5E3\"$ which is same as given\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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