document.write( "Question 103815This question is from textbook Intermediate Algebra
\n" ); document.write( ": Hello Tutors,
\n" ); document.write( "Here is another Quadratic formula problem I seriously need your help on.\r
\n" ); document.write( "\n" ); document.write( "Directions from the Professor are as follows;
\n" ); document.write( "Make sure that your work is demonstrating the solving method given in the instructions. Use the Insert and Symbols menus in Word to present the radical √ and plus/minus ± symbols. Remember that radicands must be enclosed within [ ]. Typing your work vertically is preferred but optional. If you choose to type horizontally, make sure you are appropriately using grouping symbols.\r
\n" ); document.write( "\n" ); document.write( "Here is the Problem:\r
\n" ); document.write( "\n" ); document.write( "Solve by using the Quadratic Formula;
\n" ); document.write( "x^2 - 7x - 1 + -7 Thank You! \n" ); document.write( "
Algebra.Com's Answer #75494 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"x%5E2+-+7x+-+1+%2B+-7=0\" Start with the given equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+7x+-+8=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 \"x%5E2-7%2Ax-8=0\" ( notice \"a=1\", \"b=-7\", and \"c=-8\")
\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%2A-8+%29%29%2F%282%2A1%29\" Plug in a=1, b=-7, and c=-8
\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%2A-8+%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%2A-8+%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%2B32+%29%29%2F%282%2A1%29\" Multiply \"-4%2A-8%2A1\" to get \"32\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%287+%2B-+sqrt%28+81+%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-+9%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-+9%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+9%29%2F2\" or \"x+=+%287+-+9%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+9%29%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=16%2F2\" Add the terms in the numerator
\n" ); document.write( "
\n" ); document.write( " \"x=8\" Divide
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So one answer is
\n" ); document.write( "
\n" ); document.write( " \"x=8\"
\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+-+9%29%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=-2%2F2\" Subtract the terms in the numerator
\n" ); document.write( "
\n" ); document.write( " \"x=-1\" Divide
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So another answer is
\n" ); document.write( "
\n" ); document.write( " \"x=-1\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So our solutions are:
\n" ); document.write( "
\n" ); document.write( " \"x=8\" or \"x=-1\"
\n" ); document.write( "
\n" ); document.write( "

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