document.write( "Question 104637: solve the following equation for x\r
\n" ); document.write( "\n" ); document.write( "7x^2-15X+5=3 \n" ); document.write( "
Algebra.Com's Answer #76149 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"7x%5E2-15X%2B5=3\" Start with the given equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"7x%5E2-15X%2B5-3=0\" Subtract 3 from both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"7x%5E2-15X%2B2=0\" Combine like terms\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " Starting with the general quadratic
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " the general solution using the quadratic equation is:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So lets solve \"7%2Ax%5E2-15%2Ax%2B2=0\" ( notice \"a=7\", \"b=-15\", and \"c=2\")
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28--15+%2B-+sqrt%28+%28-15%29%5E2-4%2A7%2A2+%29%29%2F%282%2A7%29\" Plug in a=7, b=-15, and c=2
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%2815+%2B-+sqrt%28+%28-15%29%5E2-4%2A7%2A2+%29%29%2F%282%2A7%29\" Negate -15 to get 15
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%2815+%2B-+sqrt%28+225-4%2A7%2A2+%29%29%2F%282%2A7%29\" Square -15 to get 225 (note: remember when you square -15, you must square the negative as well. This is because \"%28-15%29%5E2=-15%2A-15=225\".)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%2815+%2B-+sqrt%28+225%2B-56+%29%29%2F%282%2A7%29\" Multiply \"-4%2A2%2A7\" to get \"-56\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%2815+%2B-+sqrt%28+169+%29%29%2F%282%2A7%29\" Combine like terms in the radicand (everything under the square root)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%2815+%2B-+13%29%2F%282%2A7%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%2815+%2B-+13%29%2F14\" Multiply 2 and 7 to get 14
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So now the expression breaks down into two parts
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%2815+%2B+13%29%2F14\" or \"x+=+%2815+-+13%29%2F14\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Lets look at the first part:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=%2815+%2B+13%29%2F14\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=28%2F14\" Add the terms in the numerator
\n" ); document.write( "
\n" ); document.write( " \"x=2\" Divide
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So one answer is
\n" ); document.write( "
\n" ); document.write( " \"x=2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Now lets look at the second part:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=%2815+-+13%29%2F14\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=2%2F14\" Subtract the terms in the numerator
\n" ); document.write( "
\n" ); document.write( " \"x=1%2F7\" Divide
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So another answer is
\n" ); document.write( "
\n" ); document.write( " \"x=1%2F7\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So our solutions are:
\n" ); document.write( "
\n" ); document.write( " \"x=2\" or \"x=1%2F7\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "
\n" );