document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131444>Question 1131444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve The Equations and Check:\r<BR>\n" );
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document.write( "a)\sqrt(q+2)=7\r<BR>\n" );
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document.write( "b)\sqrt(5x-1)+3=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748103 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)sqrt(q+2)=7 <BR>\n" );
document.write( "square both sides to get q+2 = 49<BR>\n" );
document.write( "subtract 2 from both sides to get q = 47<BR>\n" );
document.write( "sqrt(47+2) = 7 becomes sqrt(49) = 7 becomes 7 = 7, confirming solution is good.<BR>\n" );
document.write( "solution is q = 7.\r<BR>\n" );
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document.write( "b)sqrt(5x-1)+3=0<BR>\n" );
document.write( "subtract 3 from both sides to get sqrt(5x-1) = -3<BR>\n" );
document.write( "square both sides to get 5x-1 = 9<BR>\n" );
document.write( "add 1 to both sides to get 5x = 10<BR>\n" );
document.write( "divide both sides by 5 to get x = 2<BR>\n" );
document.write( "sqrt(5*2-1) + 3 = 0 becomes sqrt(9) + 3 = 0 becomes 3 + 3 = 0 becomes 9 = 0 which is not true which means there is no solution.\r<BR>\n" );
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document.write( "you can argue that sqrt(9) is plus or minus 3, but that's not true because of a mathematical quirk that says that sqrt of a number is only the positive root and not the negativfe root.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "if you are given x^2 = 9, then you can solve for x to get x = plus or minus 3.\r<BR>\n" );
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document.write( "but, if you are given that x = sqrt(9), then the only solution is x = 3.<BR>\n" );
document.write( "x = -3 is not a solution.\r<BR>\n" );
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document.write( "the positive square root is called the principal square root.\r<BR>\n" );
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document.write( "here's an explanation from quora.\r<BR>\n" );
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document.write( "Every positive real number has two square roots; one is positive and the other is negative.  In addition, a square root of a number is one of its two equal factors, for example, 2 is a square root of 4 because (2)(2) = 4, but &#8210;2 is also a square root of 4 because (&#8210;2)(&#8210;2) = 4.  In general, a real number “a” is a square root of a nonnegative number “b” if a˛ = b. By definition, the symbol &#8730; b  is used to designate the nonnegative or principal square root of any nonnegative real number b, e.g., &#8730;4  = 2 is used to indicate the nonnegative or principal square root of 4,  and &#8210;&#8730;4  = &#8210;2 is used to indicate the negative square root of 4.  Although the principal square root of a positive number is only one of its two square roots, the designation “the square root” is often used to refer to the principal or nonnegative square root &#8730; b.  This is why &#8730;4  = 2,  rather than &#8210;2.\r<BR>\n" );
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document.write( "while it's true that sqrt(9) is plus or minus 3, only the principal, or positive root is used, by convention.\r<BR>\n" );
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document.write( "if you were allowed to use the negative square root, then sqrt(10-1) + 3 = 0 could become sqrt(9) + 3 = 0 which could becomes -3 + 3 = 0 which would then be true.\r<BR>\n" );
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document.write( "this is very confusing, because while it looks like you can do that, but you can't, because of the convention.\r<BR>\n" );
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document.write( "at least that's what i understand.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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