document.write( "Question 361402: I am having some difficulty with quadratic equations. The problem is, I don't understand the steps I should take to get the correct answer. Could you possibly show me each step I should take to find the anwer? I appreciate anyone and everyone's help!\r
\n" ); document.write( "\n" ); document.write( "Section 11.4, #6\r
\n" ); document.write( "\n" ); document.write( "Direction: Solve the equation by making an appropriate substitution. \r
\n" ); document.write( "\n" ); document.write( "(2x-4 )^2-6(2x-4)-7=0 (it should say (2x-4) squared) \r
\n" ); document.write( "\n" ); document.write( "The correct answer according to the book is: {3/2. 11/2} \n" ); document.write( "
Algebra.Com's Answer #257705 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"%282x-4+%29%5E2-6%282x-4%29-7=0\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2-16x%2B16-6%282x-4%29-7=0\" FOIL\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2-16x%2B16-12x%2B24-7=0\" Distribute.\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2-28x%2B33=0\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "Now let's solve the equation using the quadratic formula.\r
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\n" ); document.write( "\n" ); document.write( "For more help with the Quadratic Formula, check out this solver\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%5E2-28%2Ax%2B33=0\" ( notice \"a=4\", \"b=-28\", and \"c=33\")
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\n" ); document.write( " \"x+=+%28--28+%2B-+sqrt%28+%28-28%29%5E2-4%2A4%2A33+%29%29%2F%282%2A4%29\" Plug in a=4, b=-28, and c=33
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\n" ); document.write( " \"x+=+%2828+%2B-+sqrt%28+%28-28%29%5E2-4%2A4%2A33+%29%29%2F%282%2A4%29\" Negate -28 to get 28
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\n" ); document.write( " \"x+=+%2828+%2B-+sqrt%28+784-4%2A4%2A33+%29%29%2F%282%2A4%29\" Square -28 to get 784 (note: remember when you square -28, you must square the negative as well. This is because \"%28-28%29%5E2=-28%2A-28=784\".)
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\n" ); document.write( " \"x+=+%2828+%2B-+sqrt%28+784%2B-528+%29%29%2F%282%2A4%29\" Multiply \"-4%2A33%2A4\" to get \"-528\"
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\n" ); document.write( " \"x+=+%2828+%2B-+sqrt%28+256+%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+=+%2828+%2B-+16%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+=+%2828+%2B-+16%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+=+%2828+%2B+16%29%2F8\" or \"x+=+%2828+-+16%29%2F8\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%2828+%2B+16%29%2F8\"
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\n" ); document.write( " \"x=44%2F8\" Add the terms in the numerator
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\n" ); document.write( " \"x=11%2F2\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=11%2F2\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%2828+-+16%29%2F8\"
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\n" ); document.write( " \"x=12%2F8\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=3%2F2\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=3%2F2\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=11%2F2\" or \"x=3%2F2\"
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