document.write( "Question 6428: I need help with these problems can you solve these out for me in steps?\r
\n" ); document.write( "\n" ); document.write( "Set 5\r
\n" ); document.write( "\n" ); document.write( "1. factor completely: x to the 2nd power -7x -30\r
\n" ); document.write( "\n" ); document.write( "2. factor completely: x to the 2nd power + 4x -16\r
\n" ); document.write( "\n" ); document.write( "3. factor completely: 2x to the 2nd power -11x+5\r
\n" ); document.write( "\n" ); document.write( "4. factor completely: 4x to the 2nd power +20x-24\r
\n" ); document.write( "\n" ); document.write( "5. factor completely: 4m to the 2nd power - 9\r
\n" ); document.write( "\n" ); document.write( "6. factor completely: 16a to the 2nd power - 25b to the 2nd power\r
\n" ); document.write( "\n" ); document.write( "7. solve by factoring: x to the 2nd power -x-12=0\r
\n" ); document.write( "\n" ); document.write( "8. solve by factoring: 2c to the 2nd power -5=-9c\r
\n" ); document.write( "\n" ); document.write( "9. solve the equation:(x+6)(x-7)(x-8)(x+9)=0\r
\n" ); document.write( "\n" ); document.write( "10. find the dimensions of the rectangle if the width is 3 feet less than the length and the area is 40ft to the 2nd power \n" ); document.write( "
Algebra.Com's Answer #3509 by ichudov(507)\"\" \"About 
You can put this solution on YOUR website!
I'll do a couple for you....\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: x=-6,x=7,x=8,x=-9.
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  • Graphical form: Equation \"%28x%2B6%29%2A%28x-7%29%2A%28x-8%29%2A%28x%2B9%29=0\" was fully solved.
  • Text form: (x+6)*(x-7)*(x-8)*(x+9)=0 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+%28x%2B6%29%2A%28x-7%29%2A%28x-8%29%2A%28x%2B9%29=0+%29\"
    For tutors: simplify_cartoon( (x+6)*(x-7)*(x-8)*(x+9)=0 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"highlight_red%28+%28x%2B6%29+%29%2A%28x-7%29%2A%28x-8%29%2A%28x%2B9%29=0\".
Notes known roots (x-(-6))
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Look at \"highlight_red%28+%28highlight_red%28+1+%29%29%2A%28x-7%29%2A%28x-8%29%2A%28x%2B9%29+%29=0\".
Remove unneeded parentheses around factor \"highlight_red%28+1+%29\"
It becomes \"highlight_green%28+1+%29%2A%28x-7%29%2A%28x-8%29%2A%28x%2B9%29=0\".
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Look at \"highlight_red%28+1+%29%2A%28x-7%29%2A%28x-8%29%2A%28x%2B9%29=0\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"%28x-7%29%2A%28x-8%29%2A%28x%2B9%29=0\".
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Look at \"highlight_red%28+%28x-7%29+%29%2A%28x-8%29%2A%28x%2B9%29=0\".
Notes known roots (x-(7))
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Look at \"highlight_red%28+%28highlight_red%28+1+%29%29%2A%28x-8%29%2A%28x%2B9%29+%29=0\".
Remove unneeded parentheses around factor \"highlight_red%28+1+%29\"
It becomes \"highlight_green%28+1+%29%2A%28x-8%29%2A%28x%2B9%29=0\".
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Look at \"highlight_red%28+1+%29%2A%28x-8%29%2A%28x%2B9%29=0\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"%28x-8%29%2A%28x%2B9%29=0\".
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Look at \"highlight_red%28+%28x-8%29+%29%2A%28x%2B9%29=0\".
Notes known roots (x-(8))
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Look at \"highlight_red%28+%28highlight_red%28+1+%29%29%2A%28x%2B9%29+%29=0\".
Remove unneeded parentheses around factor \"highlight_red%28+1+%29\"
It becomes \"highlight_green%28+1+%29%2A%28x%2B9%29=0\".
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Look at \"highlight_red%28+1+%29%2A%28x%2B9%29=0\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"%28x%2B9%29=0\".
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Look at \"highlight_red%28+%28x%2B9%29+%29=0\".
Remove unneeded parentheses around terms \"highlight_red%28+x+%29\",\"highlight_red%28+9+%29\"
It becomes \"highlight_green%28+x+%29%2Bhighlight_green%28+9+%29=0\".
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Look at \"highlight_red%28+x%2B9+%29=0\".
Solved linear equation \"highlight_red%28+x%2B9=0+%29\" equivalent to x+9 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=-6,x=7,x=8,x=-9.

Universal Simplifier and Solver

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Done!

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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"2x%5E2%2B-11x%2B5+=+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=%28-11%29%5E2-4%2A2%2A5=81\".
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\n" ); document.write( " Discriminant d=81 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--11%2B-sqrt%28+81+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+5\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-11%29-sqrt%28+81+%29%29%2F2%5C2+=+0.5\"
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\n" ); document.write( " Quadratic expression \"2x%5E2%2B-11x%2B5\" can be factored:
\n" ); document.write( " \"2x%5E2%2B-11x%2B5+=+2%28x-5%29%2A%28x-0.5%29\"
\n" ); document.write( " Again, the answer is: 5, 0.5.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-11%2Ax%2B5+%29\"
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