document.write( "Question 247279: How would one go about solving sqrt(2x-1) + sqrt(x) = 2 \n" ); document.write( "
Algebra.Com's Answer #180784 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
You get to square everything and probably complete the square to solve.
\n" ); document.write( "first subtract sqrt(2x-1) from both sides.
\n" ); document.write( "Why? because you get that nice sqrt(x) all by itself on one side
\n" ); document.write( " sqrt(x) = 2- sqrt(2x-1)
\n" ); document.write( "now square the whole mess
\n" ); document.write( "(2- sqrt(2x-1))*(2- sqrt(2x-1))
\n" ); document.write( "use foil
\n" ); document.write( "first
\n" ); document.write( "2*2=4
\n" ); document.write( "Outside
\n" ); document.write( "2*(-sqrt(2x-1)
\n" ); document.write( "inside
\n" ); document.write( "2*(-sqrt(2x-1)
\n" ); document.write( "last
\n" ); document.write( "(-sqrt(2x-1))(-sqrt(2x-1))
\n" ); document.write( "2x-1
\n" ); document.write( "add them up and combine
\n" ); document.write( "x=4-2*(sqrt(2x-1)-2*(sqrt(2x-1)+2x-1
\n" ); document.write( "putting them in order
\n" ); document.write( "x=2x-4*(sqrt(2x-1))+3
\n" ); document.write( "If you think this is getting hairy we haven't begun the hairy part.
\n" ); document.write( "subtract x from both sides
\n" ); document.write( "0=x-4*(sqrt(2x-1))+3
\n" ); document.write( "now we want the x and 3 on e one side
\n" ); document.write( "so add 4*(sqrt(2x-1)) to both sides
\n" ); document.write( "4*(sqrt(2x-1))=x+3
\n" ); document.write( "divide both sides by 4
\n" ); document.write( "sqrt(2x-1)=(x+3)/4
\n" ); document.write( "square everything
\n" ); document.write( "2x-1=(x+3)^2/16
\n" ); document.write( "expand the terms on the right
\n" ); document.write( "2x-1=x^2/16+6x/16+9/16
\n" ); document.write( "believe it or not bring everything over to the left side to get ready for completing the square\r
\n" ); document.write( "\n" ); document.write( "2x-1-x^2/16-6x/16-9/16=0
\n" ); document.write( "combine terms
\n" ); document.write( "32x/16-16/16-x^2/16-6x/16-9/16=0\r
\n" ); document.write( "\n" ); document.write( "-x^2/16+13x/8-25/16=0\r
\n" ); document.write( "\n" ); document.write( "multiply by -16 or divide by -1/16
\n" ); document.write( "x^2-26x+25=0
\n" ); document.write( "subtract 25 from both sides.
\n" ); document.write( "complete the square
\n" ); document.write( "x^2-26x=-25
\n" ); document.write( "add (26/2)^2to both sides= 169
\n" ); document.write( "x^2-26x+169=144
\n" ); document.write( "factor
\n" ); document.write( "(x-13)=12
\n" ); document.write( "x=13+\-12
\n" ); document.write( "x=13+12
\n" ); document.write( "x=13-12
\n" ); document.write( "x=1
\n" ); document.write( "x=25
\n" ); document.write( "now we have to test both solutions to see if they fit in the original equation
\n" ); document.write( "sqrt(2x-1) + sqrt(x) = 2
\n" ); document.write( "let's check x=1
\n" ); document.write( "sqrt(2(1)-1)+sqrt(1)=2
\n" ); document.write( "sqrt(1)+sqrt(1)=2
\n" ); document.write( "1+1=2
\n" ); document.write( "yes
\n" ); document.write( "let's test 25
\n" ); document.write( "sqrt(2x-1) + sqrt(x) = 2
\n" ); document.write( "sqrt(50-1)+sqrt(25)=2
\n" ); document.write( "sqrt(49)+sqrt(25)=2
\n" ); document.write( "+\-7+\-5
\n" ); document.write( "+7-5=2
\n" ); document.write( "but the others
\n" ); document.write( "+7+5=12
\n" ); document.write( "-7-5=-12
\n" ); document.write( "-7+5=-2 don't work\r
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