document.write( "Question 857661: Solve using the quadratic equation \"3x%5E2%2B2.5x=12.5\" \n" ); document.write( "
Algebra.Com's Answer #516704 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
3x^2+2.5x-12.5=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 \"6%2Ax%5E2%2B5%2Ax-25=0\" ( notice \"a=6\", \"b=5\", and \"c=-25\")
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\n" ); document.write( " \"x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A6%2A-25+%29%29%2F%282%2A6%29\" Plug in a=6, b=5, and c=-25
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\n" ); document.write( " \"x+=+%28-5+%2B-+sqrt%28+25-4%2A6%2A-25+%29%29%2F%282%2A6%29\" Square 5 to get 25
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\n" ); document.write( " \"x+=+%28-5+%2B-+sqrt%28+25%2B600+%29%29%2F%282%2A6%29\" Multiply \"-4%2A-25%2A6\" to get \"600\"
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\n" ); document.write( " \"x+=+%28-5+%2B-+sqrt%28+625+%29%29%2F%282%2A6%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%28-5+%2B-+25%29%2F%282%2A6%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+=+%28-5+%2B-+25%29%2F12\" Multiply 2 and 6 to get 12
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%28-5+%2B+25%29%2F12\" or \"x+=+%28-5+-+25%29%2F12\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%28-5+%2B+25%29%2F12\"
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\n" ); document.write( " \"x=20%2F12\" Add the terms in the numerator
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\n" ); document.write( " \"x=5%2F3\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=5%2F3\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%28-5+-+25%29%2F12\"
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\n" ); document.write( " \"x=-30%2F12\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-5%2F2\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-5%2F2\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=5%2F3\" or \"x=-5%2F2\"
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"3x%5E2%2B2.5x%2B-12.5+=+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=%282.5%29%5E2-4%2A3%2A-12.5=156.25\".
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\n" ); document.write( " Discriminant d=156.25 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-2.5%2B-sqrt%28+156.25+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%282.5%29%2Bsqrt%28+156.25+%29%29%2F2%5C3+=+1.66666666666667\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%282.5%29-sqrt%28+156.25+%29%29%2F2%5C3+=+-2.5\"
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\n" ); document.write( " Quadratic expression \"3x%5E2%2B2.5x%2B-12.5\" can be factored:
\n" ); document.write( " \"3x%5E2%2B2.5x%2B-12.5+=+3%28x-1.66666666666667%29%2A%28x--2.5%29\"
\n" ); document.write( " Again, the answer is: 1.66666666666667, -2.5.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2.5%2Ax%2B-12.5+%29\"

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