document.write( "Question 394798: Give exact and approximate solutions to three decimal places.
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\n" ); document.write( "\n" ); document.write( "What are the exact solutions?
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\n" ); document.write( "(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)\r
\n" ); document.write( "\n" ); document.write( "What are the approximate solutions?
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\n" ); document.write( "(Use a comma to separate answers as needed. Round to the nearest thousandth as needed.)
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Algebra.Com's Answer #280119 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+4x+%2B+4+=12\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+4x+%2B+4+-+12+=+0\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+4x+-+8+=+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-8=0\" ( notice \"a=1\", \"b=-4\", and \"c=-8\")
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\n" ); document.write( " \"x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29\" Plug in a=1, b=-4, and c=-8
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\n" ); document.write( " \"x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-8+%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-8+%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%2B32+%29%29%2F%282%2A1%29\" Multiply \"-4%2A-8%2A1\" to get \"32\"
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\n" ); document.write( " \"x+=+%284+%2B-+sqrt%28+48+%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-+4%2Asqrt%283%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+=+%284+%2B-+4%2Asqrt%283%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+=+%284+%2B+4%2Asqrt%283%29%29%2F2\" or \"x+=+%284+-+4%2Asqrt%283%29%29%2F2\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=%2B4%2F2%2B4%2Asqrt%283%29%2F2\" or \"x=%2B4%2F2-4%2Asqrt%283%29%2F2\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=2%2B2%2Asqrt%283%29\" or \"x=2-2%2Asqrt%283%29\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=2%2B2%2Asqrt%283%29\" or \"x=2-2%2Asqrt%283%29\"
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\n" ); document.write( "\n" ); document.write( " the exact solutions are\r
\n" ); document.write( "\n" ); document.write( "\"x1+=+2+%2B+2sqrt%283%29+=+2%2B2%2A1.73+=+2+%2B+3.46+=+5.46+\"\r
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\n" ); document.write( "\n" ); document.write( "\"x2+=+2+-+2sqrt%283%29+=+2-2%2A1.73+=+2+-+3.46+=+-1.46+\"\r
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\n" ); document.write( "\n" ); document.write( "the approximate solutions\r
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\n" ); document.write( "\n" ); document.write( "\"x1+=+2+%2B+2sqrt%283%29+=+5.46+=+6\"\r
\n" ); document.write( "\n" ); document.write( "\"x2+=+2+-+2sqrt%283%29+=+-1.46+=+-2+\"\r
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