document.write( "Question 819823: How would you solve \"+sqrt%28+1-4x+%29=3+\" ? \n" ); document.write( "
Algebra.Com's Answer #493364 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Here's a procedure for these radcial equations:
  1. Isolate a radical (which has a variable inside).
  2. Raise each side of the equation to a power that matches the type of root. This should eliminate the isolated radical. (But if there is a radical on the other side of the equation, too, then it may not disappear.
    3. If there are still any radicals, repeat steps 1 and 2 on the new equation.
  3. At this point there should be no radicals left. Solve this equation using appropriate techniques for the type of equation it is.
  4. If at any point the equation was raised to an even power, then a check must be made!
Let's see this in action on your equation:
\n" ); document.write( "\"+sqrt%28+1-4x+%29=3+\"
\n" ); document.write( "1. Isolate.
\n" ); document.write( "Your radical is already isolated (by itself on one side).
\n" ); document.write( "2. Raise to a power.
\n" ); document.write( "Since your radical is a square root, we will square both sides:
\n" ); document.write( "\"+%28sqrt%28+1-4x+%29%29%5E2=%283%29%5E2+\"
\n" ); document.write( "which simplifies to:
\n" ); document.write( "\"1-4x+=+9\"
\n" ); document.write( "3. Any radicals?
\n" ); document.write( "No. So on to step 4.
\n" ); document.write( "4. Solve.
\n" ); document.write( "Subtracting 1 from each side:
\n" ); document.write( "-4x = 8
\n" ); document.write( "Dividing by -4:
\n" ); document.write( "x = -2
\n" ); document.write( "5. Check.
\n" ); document.write( "When we squared both sides earlier we raised them to an even power. So we must check. Use the original equation to check:
\n" ); document.write( "\"+sqrt%28+1-4x+%29=3+\"
\n" ); document.write( "Checking x = -2:
\n" ); document.write( "\"+sqrt%28+1-4%28-2%29+%29=3+\"
\n" ); document.write( "\"+sqrt%28+1%2B8+%29=3+\"
\n" ); document.write( "\"+sqrt%28+9+%29=3+\"
\n" ); document.write( "\"+3=3+\" Check!!
\n" ); document.write( "So the only solution is x = -2.
\n" ); document.write( " \n" ); document.write( "
\n" );