document.write( "Question 295330: Find all real soultions.\r
\n" ); document.write( "\n" ); document.write( "x^2+30x + 200 = 0\r
\n" ); document.write( "\n" ); document.write( "x^2 + 3x + 1 = 0\r
\n" ); document.write( "\n" ); document.write( "X^2- 6x + 1 = 0\r
\n" ); document.write( "\n" ); document.write( "3x^2 + 7x + 4 = 0 \n" ); document.write( "
Algebra.Com's Answer #212832 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
# 1\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%2B30%2Ax%2B200=0\" ( notice \"a=1\", \"b=30\", and \"c=200\")
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\n" ); document.write( " \"x+=+%28-30+%2B-+sqrt%28+%2830%29%5E2-4%2A1%2A200+%29%29%2F%282%2A1%29\" Plug in a=1, b=30, and c=200
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\n" ); document.write( " \"x+=+%28-30+%2B-+sqrt%28+900-4%2A1%2A200+%29%29%2F%282%2A1%29\" Square 30 to get 900
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\n" ); document.write( " \"x+=+%28-30+%2B-+sqrt%28+900%2B-800+%29%29%2F%282%2A1%29\" Multiply \"-4%2A200%2A1\" to get \"-800\"
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\n" ); document.write( " \"x+=+%28-30+%2B-+sqrt%28+100+%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+=+%28-30+%2B-+10%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+=+%28-30+%2B-+10%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+=+%28-30+%2B+10%29%2F2\" or \"x+=+%28-30+-+10%29%2F2\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%28-30+%2B+10%29%2F2\"
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\n" ); document.write( " \"x=-20%2F2\" Add the terms in the numerator
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\n" ); document.write( " \"x=-10\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=-10\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%28-30+-+10%29%2F2\"
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\n" ); document.write( " \"x=-40%2F2\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-20\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-20\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=-10\" or \"x=-20\"
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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%2B3%2Ax%2B1=0\" ( notice \"a=1\", \"b=3\", and \"c=1\")
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\n" ); document.write( " \"x+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29\" Plug in a=1, b=3, and c=1
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\n" ); document.write( " \"x+=+%28-3+%2B-+sqrt%28+9-4%2A1%2A1+%29%29%2F%282%2A1%29\" Square 3 to get 9
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\n" ); document.write( " \"x+=+%28-3+%2B-+sqrt%28+9%2B-4+%29%29%2F%282%2A1%29\" Multiply \"-4%2A1%2A1\" to get \"-4\"
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\n" ); document.write( " \"x+=+%28-3+%2B-+sqrt%28+5+%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+=+%28-3+%2B-+sqrt%285%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+=+%28-3+%2B-+sqrt%285%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+=+%28-3+%2B+sqrt%285%29%29%2F2\" or \"x+=+%28-3+-+sqrt%285%29%29%2F2\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=-3%2F2%2Bsqrt%285%29%2F2\" or \"x=-3%2F2-sqrt%285%29%2F2\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=-3%2F2%2Bsqrt%285%29%2F2\" or \"x=-3%2F2-sqrt%285%29%2F2\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=-3%2F2%2Bsqrt%285%29%2F2\" or \"x=-3%2F2-sqrt%285%29%2F2\"
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