document.write( "Question 887003: Solve using quadratic formula
\n" ); document.write( "y= 5x^2-8x-2\r
\n" ); document.write( "\n" ); document.write( "x= 8± sqrt ( 104 )
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\n" ); document.write( "x= 8 ± sqrt (4*26)
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\n" ); document.write( "10\r
\n" ); document.write( "\n" ); document.write( "x= 8± 2 sqrt (26)
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\n" ); document.write( "10
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\n" ); document.write( "x= 4± sqrt (26 )
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\n" ); document.write( "5\r
\n" ); document.write( "\n" ); document.write( "That is what I tried. Can you please correct me if something is wrong with my answer. \n" ); document.write( "
Algebra.Com's Answer #536302 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"5x%5E2%2B-8x%2B-2+=+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=%28-8%29%5E2-4%2A5%2A-2=104\".
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\n" ); document.write( " Discriminant d=104 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--8%2B-sqrt%28+104+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+104+%29%29%2F2%5C5+=+1.81980390271856\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-8%29-sqrt%28+104+%29%29%2F2%5C5+=+-0.219803902718557\"
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\n" ); document.write( " Quadratic expression \"5x%5E2%2B-8x%2B-2\" can be factored:
\n" ); document.write( " \"5x%5E2%2B-8x%2B-2+=+5%28x-1.81980390271856%29%2A%28x--0.219803902718557%29\"
\n" ); document.write( " Again, the answer is: 1.81980390271856, -0.219803902718557.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-8%2Ax%2B-2+%29\"
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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 \"5%2Ax%5E2-8%2Ax-2=0\" ( notice \"a=5\", \"b=-8\", and \"c=-2\")
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\n" ); document.write( " \"x+=+%28--8+%2B-+sqrt%28+%28-8%29%5E2-4%2A5%2A-2+%29%29%2F%282%2A5%29\" Plug in a=5, b=-8, and c=-2
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\n" ); document.write( " \"x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%2A5%2A-2+%29%29%2F%282%2A5%29\" Negate -8 to get 8
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\n" ); document.write( " \"x+=+%288+%2B-+sqrt%28+64-4%2A5%2A-2+%29%29%2F%282%2A5%29\" Square -8 to get 64 (note: remember when you square -8, you must square the negative as well. This is because \"%28-8%29%5E2=-8%2A-8=64\".)
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\n" ); document.write( " \"x+=+%288+%2B-+sqrt%28+64%2B40+%29%29%2F%282%2A5%29\" Multiply \"-4%2A-2%2A5\" to get \"40\"
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\n" ); document.write( " \"x+=+%288+%2B-+sqrt%28+104+%29%29%2F%282%2A5%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%288+%2B-+2%2Asqrt%2826%29%29%2F%282%2A5%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+=+%288+%2B-+2%2Asqrt%2826%29%29%2F10\" Multiply 2 and 5 to get 10
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%288+%2B+2%2Asqrt%2826%29%29%2F10\" or \"x+=+%288+-+2%2Asqrt%2826%29%29%2F10\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=%2B8%2F10%2B2%2Asqrt%2826%29%2F10\" or \"x=%2B8%2F10-2%2Asqrt%2826%29%2F10\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=4%2F5%2Bsqrt%2826%29%2F5\" or \"x=4%2F5-sqrt%2826%29%2F5\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=4%2F5%2Bsqrt%2826%29%2F5\" or \"x=4%2F5-sqrt%2826%29%2F5\"
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