document.write( "Question 178168: Solve √(2x+3) - √(2x)=1 \n" ); document.write( "

Algebra.Com's Answer #133126 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve √(2x+3) - √(2x)=1\r
\n" ); document.write( "\n" ); document.write( "Square both sides to get:\r
\n" ); document.write( "\n" ); document.write( "2x+3 -2sqrt(2x(2x+3) - 2x = 1\r
\n" ); document.write( "\n" ); document.write( "Combine:
\n" ); document.write( "-2sqrt(4x^2+6x) = -2\r
\n" ); document.write( "\n" ); document.write( "sqrt(4x^2+6x) = 1
\n" ); document.write( "Square both sides to get:\r
\n" ); document.write( "\n" ); document.write( "4x^2 + 6x = 1\r
\n" ); document.write( "\n" ); document.write( "Rearrange:
\n" ); document.write( "4x^2 + 6x -1 = 0
\n" ); document.write( "Use quadratic formula:\r
\n" ); document.write( "\n" ); document.write( "x = [-6 +- sqrt(36 - 4*4*-1] / 8\r
\n" ); document.write( "\n" ); document.write( "x = [-6 +- sqrt(52)/8\r
\n" ); document.write( "\n" ); document.write( "x = [-6 +- 2sqrt(13)]/8\r
\n" ); document.write( "\n" ); document.write( "x = [3 +- sqrt(13)]/4
\n" ); document.write( "============================
\n" ); document.write( "Check the answers to see if any are extraneous.
\n" ); document.write( "===============================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

\n" );