document.write( "Question 107339: I believe I have this correct. Can you please check it for me.\r
\n" ); document.write( "\n" ); document.write( "3x^2+5x-3=x
\n" ); document.write( "3x^2+5x-3-x=0
\n" ); document.write( "3x^2+4x=3\r
\n" ); document.write( "\n" ); document.write( "Thank You \n" ); document.write( "
Algebra.Com's Answer #78200 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given:
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\n" ); document.write( "3x^2+5x-3=x <=== OK
\n" ); document.write( "3x^2+5x-3-x=0 <=== OK
\n" ); document.write( "3x^2+4x=3 <=== OK, but why not solve for x by using the quadratic formula
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\n" ); document.write( "Start with your second equation:
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\n" ); document.write( "3x^2 + 5x - 3 -x = 0
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\n" ); document.write( "Combine the 5x and -x to get +4x. This reduces the equation to:
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\n" ); document.write( "3x^2 + 4x - 3 = 0
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\n" ); document.write( "Now recognize that this is in the standard quadratic form of ax^2 + bx + c = 0 in which (by
\n" ); document.write( "comparing your equation with the standard quadratic form) a = 3, b = 4, and c = -3.
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\n" ); document.write( "The quadratic formula says that when you have a quadratic equation in the standard quadratic
\n" ); document.write( "form, the answer for x 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( "So to get the answer for x all you have to do is appropriately substitute 3 for a, 4 for b,
\n" ); document.write( "and -3 for c in the answer equation. When you do that you get:
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\n" ); document.write( "\"x+=+%28-%284%29%2B-sqrt%284%5E2+-+4%2A3%2A%28-3%29%29%29%2F%282%2A3%29\"
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\n" ); document.write( "notice that -(4) is just -4. Then within the radical sign 4^2 is 16 and -4*3*(-3) is +36.
\n" ); document.write( "And finally in the denominator 2*3 = 6. Substitute these values into the equation and you get:
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\n" ); document.write( "\"x+=+%28-4%2B-sqrt%2816+%2B36%29%29%2F%286%29\"
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\n" ); document.write( "The terms under the radical sign add up to 52. And this 52 factors to 4*13. Substituting this
\n" ); document.write( "into the answer for x results in:
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\n" ); document.write( "\"x+=+%28-4%2B-sqrt%284%2A13%29%29%2F%286%29\"
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\n" ); document.write( "But \"sqrt%284%2A13%29+=+sqrt%284%29%2Asqrt%2813%29+=+2%2Asqrt%2813%29\"
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\n" ); document.write( "Substituting this for sqrt(4*13) further simplifies the problem to:
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4%2B-2%2Asqrt%2813%29%29%2F%286%29\"
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\n" ); document.write( "Notice that both terms in the numerator have 2 as a factor. And the denominator also has
\n" ); document.write( "2 as a factor. So, if you divide the numerator by 2 and the denominator by 2, the equation
\n" ); document.write( "for x reduces to:
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2%2B-sqrt%2813%29%29%2F%283%29\"
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\n" ); document.write( "Now you can write the two answers for x. First use the plus sign between the terms in the
\n" ); document.write( "numerator to get:
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\n" ); document.write( "\"x+=+%28-2%2Bsqrt%2813%29%29%2F%283%29\"
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\n" ); document.write( "then use the minus sign to get the other answer for x:
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\n" ); document.write( "\"x+=+%28-2-sqrt%2813%29%29%2F%283%29\"
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\n" ); document.write( "And there you have the two answers for x
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\n" ); document.write( "Hope this helps you understand the problem.
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