document.write( "Question 394489: how do i solve this x+12/x=7 \n" ); document.write( "
Algebra.Com's Answer #279896 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "\"x%2B12%2Fx=7\"...both sides multiply by \"x\"\r
\n" ); document.write( "\n" ); document.write( "\"x%2Ax+%2B%2812%2Fx%29x+=+7x\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%2Ax+%2B%2812%2Fcross%28x%29%29cross%28x%29+=+7x\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%5E2+%2B12+=+7x\"...add \"-7x\" to both sides\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%5E2++-7x+%2B12++=+7x+-+7x\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%5E2++-7x+%2B12++=+0\"...use quadratic formula\r
\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 \"x%5E2-7%2Ax%2B12=0\" ( notice \"a=1\", \"b=-7\", and \"c=12\")
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29\" Plug in a=1, b=-7, and c=12
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29\" Negate -7 to get 7
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%287+%2B-+sqrt%28+49-4%2A1%2A12+%29%29%2F%282%2A1%29\" Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because \"%28-7%29%5E2=-7%2A-7=49\".)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%287+%2B-+sqrt%28+49%2B-48+%29%29%2F%282%2A1%29\" Multiply \"-4%2A12%2A1\" to get \"-48\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%287+%2B-+sqrt%28+1+%29%29%2F%282%2A1%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+=+%287+%2B-+1%29%2F%282%2A1%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+=+%287+%2B-+1%29%2F2\" Multiply 2 and 1 to get 2
\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+=+%287+%2B+1%29%2F2\" or \"x+=+%287+-+1%29%2F2\"
\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=%287+%2B+1%29%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=8%2F2\" Add the terms in the numerator
\n" ); document.write( "
\n" ); document.write( " \"x=4\" Divide
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So one answer is
\n" ); document.write( "
\n" ); document.write( " \"x=4\"
\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=%287+-+1%29%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=6%2F2\" Subtract the terms in the numerator
\n" ); document.write( "
\n" ); document.write( " \"x=3\" Divide
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So another answer is
\n" ); document.write( "
\n" ); document.write( " \"x=3\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So our solutions are:
\n" ); document.write( "
\n" ); document.write( " \"x=4\" or \"x=3\"
\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );