document.write( "Question 116121: 2x squared + 10x = -1 \n" ); document.write( "
Algebra.Com's Answer #84441 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Let's begin this problem by getting it into the standard quadratic form:
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\n" ); document.write( "\"ax%5E2+%2B+bx+%2B+c+=+0\"
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\n" ); document.write( "You can get it into the quadratic form by adding 1 to both sides of the equation to transform it
\n" ); document.write( "to:
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\n" ); document.write( "\"2x%5E2+%2B+10x+%2B1+=+0\"
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\n" ); document.write( "By comparing this to the standard form above you can see that \"a\" corresponds to 2,
\n" ); document.write( "b corresponds to 10, and c corresponds to 1.
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\n" ); document.write( "If you have trouble factoring the original problem or you suspect that the problem may have a
\n" ); document.write( "set of complex answers, a good method to use on a quadratic equation is the quadratic formula
\n" ); document.write( "which says that for the form:
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\n" ); document.write( "\"ax%5E2+%2B+bx+%2B+c+=+0\"
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\n" ); document.write( "the solution is given by:
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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( "for this problem, if you substitute +2 for a, +10 for b, and +1 for c, you get the solution
\n" ); document.write( "as:
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\n" ); document.write( "\"x+=+%28-%2810%29+%2B-+sqrt%28+10%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29+\"
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\n" ); document.write( "Inside the radical sign the \"10%5E2+-+4%2A2%2A1\" simplifies to \"100+-+8+=+92\". Since this is
\n" ); document.write( "positive you know that the two values of x will be real. The square root of 92 is 9.591663047.
\n" ); document.write( "Substituting this into the equation for x results in:
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%2810%29+%2B-+9.591663047%29%2F%282%2A2%29+\"
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\n" ); document.write( "The -(10) is equivalent to -10 and in the denominator the 2*2 = 4. These two simplify the
\n" ); document.write( "equation for x to:
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\n" ); document.write( "\"x+=+%28-10+%2B-+9.591663047%29%2F4\"
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\n" ); document.write( "This means the two answers for x are:
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\n" ); document.write( "\"x+=+%28-10+%2B+9.591663047%29%2F4+=+-0.408336953%2F4+=+-0.102084238\"
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\n" ); document.write( "and
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-10+-+9.591663047%29%2F4++=+-19.591663047%2F4+=+-4.897915762\"
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\n" ); document.write( "Hope this helps you to do the problem. If you want to get the answers in terms of radicals,
\n" ); document.write( "you can replace \"sqrt%2892%29\" by \"2%2Asqrt%2823%29\" and your answers will be:
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\n" ); document.write( "\"x+=+%28-%2810%29+%2B-+2%2Asqrt%2823%29%29%2F%282%2A2%29+\"
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\n" ); document.write( "Which you can simplify down to:
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\n" ); document.write( "\"x+=+%28-5%2B-sqrt%2823%29%29%2F2\"
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