document.write( "Question 105072: Tutor, \r
\n" ); document.write( "\n" ); document.write( "I am think this is incorrect could you please help me with this problem: \r
\n" ); document.write( "\n" ); document.write( "Solve by using the quadratic formula\r
\n" ); document.write( "\n" ); document.write( "4x^2 - 3x + = 0 (no real number solutions?)
\n" ); document.write( "and
\n" ); document.write( "X^2 + x - 2 = 0 (is this 1,2 ?) \r
\n" ); document.write( "\n" ); document.write( "Any help is appreciated. \n" ); document.write( "
Algebra.Com's Answer #76447 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Something seems like it's missing...\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 \"4%2Ax%5E2-3%2Ax%2B0=0\" (note: since the polynomial does not have a constant term, the 3rd coefficient is zero. In other words, c=0. So that means the polynomial really looks like \"4%2Ax%5E2-3%2Ax%2B0=0\" notice \"a=4\", \"b=-3\", and \"c=0\")
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\n" ); document.write( " \"x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A0+%29%29%2F%282%2A4%29\" Plug in a=4, b=-3, and c=0
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A0+%29%29%2F%282%2A4%29\" Negate -3 to get 3
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9-4%2A4%2A0+%29%29%2F%282%2A4%29\" Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because \"%28-3%29%5E2=-3%2A-3=9\".)
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9%2B0+%29%29%2F%282%2A4%29\" Multiply \"-4%2A0%2A4\" to get \"0\"
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9+%29%29%2F%282%2A4%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%283+%2B-+3%29%2F%282%2A4%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+=+%283+%2B-+3%29%2F8\" Multiply 2 and 4 to get 8
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%283+%2B+3%29%2F8\" or \"x+=+%283+-+3%29%2F8\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%283+%2B+3%29%2F8\"
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\n" ); document.write( " \"x=6%2F8\" Add the terms in the numerator
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\n" ); document.write( " \"x=3%2F4\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=3%2F4\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%283+-+3%29%2F8\"
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\n" ); document.write( " \"x=0%2F8\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=0\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=0\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=3%2F4\" or \"x=0\"
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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( "
\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( "
\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( "
\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%2Bx-2=0\" ( notice \"a=1\", \"b=1\", and \"c=-2\")
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\n" ); document.write( " \"x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A-2+%29%29%2F%282%2A1%29\" Plug in a=1, b=1, and c=-2
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\n" ); document.write( " \"x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A-2+%29%29%2F%282%2A1%29\" Square 1 to get 1
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\n" ); document.write( " \"x+=+%28-1+%2B-+sqrt%28+1%2B8+%29%29%2F%282%2A1%29\" Multiply \"-4%2A-2%2A1\" to get \"8\"
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\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-1+%2B-+sqrt%28+9+%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+=+%28-1+%2B-+3%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+=+%28-1+%2B-+3%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( "
\n" ); document.write( " \"x+=+%28-1+%2B+3%29%2F2\" or \"x+=+%28-1+-+3%29%2F2\"
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\n" ); document.write( "
\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%28-1+%2B+3%29%2F2\"
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\n" ); document.write( " \"x=2%2F2\" Add the terms in the numerator
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\n" ); document.write( " \"x=1\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=1\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%28-1+-+3%29%2F2\"
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\n" ); document.write( " \"x=-4%2F2\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-2\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-2\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=1\" or \"x=-2\"
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