document.write( "Question 241004: finding square roots\r
\n" ); document.write( "\n" ); document.write( "1) x^2=60\r
\n" ); document.write( "\n" ); document.write( "2) x^2-9=16\r
\n" ); document.write( "\n" ); document.write( "3) 4x^2+7=23\r
\n" ); document.write( "\n" ); document.write( "4) x^2/6-2=0
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #176592 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
In general, there are three ways to solve quadratic equations:
  • Complete the square and find the square root fo each side.
  • Get one side equal to zero and
    • Factor; or
    • Use the Quadratic Formula
Most the the time completing the square is the most difficult. But when there is no x term, just \"x%5E2\" terms, then completing the square is fairly easy. Since all of your problems have no x terms, we will complete the square.

\n" ); document.write( "To complete the square, get the x terms on one side and form a perfect square. Then find the square root of each side and solve.

\n" ); document.write( "1) \"x%5E2=60\"
\n" ); document.write( "The x terms are already on the left and \"x%5E2\" is already a perfect square. So we will find the square root of each side:
\n" ); document.write( "\"sqrt%28x%5E2%29+=+sqrt%2860%29\"
\n" ); document.write( "A very common mistake is to think that \"sqrt%28x%5E2%29+=+x\". It is not. \"sqrt%28x%5E2%29+=+abs%28x%29\"! So our equation simplifies to:
\n" ); document.write( "\"abs%28x%29+=+sqrt%2860%29\"
\n" ); document.write( "Solving an absolute value equation requires two equations:
\n" ); document.write( "\"x+=+sqrt%2860%29\" or x = \"-sqrt%2860%29\"
\n" ); document.write( "Since \"sqrt%2860%29+=+sqrt%284%2A15%29+=+sqrt%284%29%2Asqrt%2815%29+=+2sqrt%2815%29\" our final answer is
\n" ); document.write( "\"x+=+2sqrt%2815%29\" or \"x+=+-2sqrt%2815%29\"

\n" ); document.write( "On the remainder of the problems I will be using the same steps:
  1. Complete the square
    1. Gather the x terms on one side
    2. Form a perfect square
  2. Find the square root of each side
  3. Solve
So there will be fewer comments on the rest of the problems.
\r
\n" ); document.write( "\n" ); document.write( "2) \"x%5E2-9=16\"
\n" ); document.write( "Add 9 to both sides
\n" ); document.write( "\"x%5E2+=+25\"
\n" ); document.write( "\"sqrt%28x%5E2%29+=++sqrt%2825%29\"
\n" ); document.write( "\"abs%28x%29+=+5\"
\n" ); document.write( "\"x+=+5\" or \"x+=+-5\"
\r
\n" ); document.write( "\n" ); document.write( "3) \"4x%5E2%2B7=23\"
\n" ); document.write( "Subtract 7 from each side
\n" ); document.write( "\"4x%5E2+=+16\"
\n" ); document.write( "Divide both sides by 4
\n" ); document.write( "\"x%5E2+=+4\"
\n" ); document.write( "\"sqrt%28x%5E2%29+=+sqrt%284%29\"
\n" ); document.write( "\"abs%28x%29+=+2\"
\n" ); document.write( "\"x+-+2\" or \"x+=+-2\"
\r
\n" ); document.write( "\n" ); document.write( "4) \"x%5E2%2F6-2=0\"
\n" ); document.write( "Add 2 to both sides
\n" ); document.write( "\"x%5E2%2F6+=+2\"
\n" ); document.write( "Multiply both sides by 6
\n" ); document.write( "\"x%5E2+=+12\"
\n" ); document.write( "\"sqrt%28x%5E2%29+=+sqrt%2812%29\"
\n" ); document.write( "\"abs%28x%29+=+sqrt%2812%29\"
\n" ); document.write( "\"x+=+sqrt%2812%29\" or \"x+=+-sqrt%2812%29\"
\n" ); document.write( "Since \"sqrt%2812%29+=+sqrt%284%2A3%29+=+sqrt%284%29%2Asqrt%283%29+=+2sqrt%283%29\"
\n" ); document.write( "\"x+=+2sqrt%283%29\" or \"x+=+-2sqrt%283%29\"
\n" ); document.write( " \n" ); document.write( "
\n" );