document.write( "Question 397228: the quadratic equation exercises that are attached to this note and demonstrate how your quadratic equation is solved by the Factoring Method. Explain your steps. Demonstrate how your quadratic equation expression is solved by the Square Root Property. Explain your steps. Two quadratic equations (similar to the ones you chose to explain above) for your classmates to solve using the algorithms to work with quadratic equations.
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Algebra.Com's Answer #281589 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+18x+%2B+81=+34\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+18x+%2B+81-34=0\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+18x+%2B+47=0\"\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"x%5E2-18%2Ax%2B47=0\" ( notice \"a=1\", \"b=-18\", and \"c=47\")
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\n" ); document.write( " \"x+=+%28--18+%2B-+sqrt%28+%28-18%29%5E2-4%2A1%2A47+%29%29%2F%282%2A1%29\" Plug in a=1, b=-18, and c=47
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\n" ); document.write( " \"x+=+%2818+%2B-+sqrt%28+%28-18%29%5E2-4%2A1%2A47+%29%29%2F%282%2A1%29\" Negate -18 to get 18
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\n" ); document.write( " \"x+=+%2818+%2B-+sqrt%28+324-4%2A1%2A47+%29%29%2F%282%2A1%29\" Square -18 to get 324 (note: remember when you square -18, you must square the negative as well. This is because \"%28-18%29%5E2=-18%2A-18=324\".)
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\n" ); document.write( " \"x+=+%2818+%2B-+sqrt%28+324%2B-188+%29%29%2F%282%2A1%29\" Multiply \"-4%2A47%2A1\" to get \"-188\"
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\n" ); document.write( " \"x+=+%2818+%2B-+sqrt%28+136+%29%29%2F%282%2A1%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%2818+%2B-+2%2Asqrt%2834%29%29%2F%282%2A1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%2818+%2B-+2%2Asqrt%2834%29%29%2F2\" Multiply 2 and 1 to get 2
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%2818+%2B+2%2Asqrt%2834%29%29%2F2\" or \"x+=+%2818+-+2%2Asqrt%2834%29%29%2F2\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=%2B18%2F2%2B2%2Asqrt%2834%29%2F2\" or \"x=%2B18%2F2-2%2Asqrt%2834%29%2F2\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=9%2Bsqrt%2834%29\" or \"x=9-sqrt%2834%29\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=9%2Bsqrt%2834%29\" or \"x=9-sqrt%2834%29\"
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\n" ); document.write( "\n" ); document.write( "\"t%5E2+-+4t+%2B+4=+25\"\r
\n" ); document.write( "\n" ); document.write( "\"t%5E2+-+4t+%2B+4-+25=0\"\r
\n" ); document.write( "\n" ); document.write( "\"t%5E2+-+4t+-+21=0\"\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"x%5E2-4%2Ax-21=0\" ( notice \"a=1\", \"b=-4\", and \"c=-21\")
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\n" ); document.write( " \"x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29\" Plug in a=1, b=-4, and c=-21
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\n" ); document.write( " \"x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29\" Negate -4 to get 4
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\n" ); document.write( " \"x+=+%284+%2B-+sqrt%28+16-4%2A1%2A-21+%29%29%2F%282%2A1%29\" Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because \"%28-4%29%5E2=-4%2A-4=16\".)
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\n" ); document.write( " \"x+=+%284+%2B-+sqrt%28+16%2B84+%29%29%2F%282%2A1%29\" Multiply \"-4%2A-21%2A1\" to get \"84\"
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\n" ); document.write( " \"x+=+%284+%2B-+sqrt%28+100+%29%29%2F%282%2A1%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%284+%2B-+10%29%2F%282%2A1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%284+%2B-+10%29%2F2\" Multiply 2 and 1 to get 2
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( "
\n" ); document.write( " \"x+=+%284+%2B+10%29%2F2\" or \"x+=+%284+-+10%29%2F2\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%284+%2B+10%29%2F2\"
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\n" ); document.write( " \"x=14%2F2\" Add the terms in the numerator
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\n" ); document.write( " \"x=7\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=7\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%284+-+10%29%2F2\"
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\n" ); document.write( " \"x=-6%2F2\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-3\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-3\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=7\" or \"x=-3\"
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