document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61078>Question 61078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help? <BR>\n" );
document.write( "Solve the following equations. Leave radicals in radical form ( do not calculate their approximate values.)\r<BR>\n" );
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document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+x%2B6-4=x ALIGN=MIDDLE  ALT=\"sqrt+x%2B6-4=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29sqrt%283x%2B1%29=%285%29sqrt%28x%5E2-2x-5%29 ALIGN=MIDDLE  ALT=\"%285%29sqrt%283x%2B1%29=%285%29sqrt%28x%5E2-2x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the 5's should be at the tip of the radical sign)\r<BR>\n" );
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document.write( "c. (x+6)^2/5+2=3\r<BR>\n" );
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document.write( "Thank you for your help!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41998 by </B><A HREF=/tutors/aboutme.mpl?userid=uma><B>uma(370)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=uma><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=41998\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) sqrt(x+6) - 4 = x<BR>\n" );
document.write( "Addinfg 4 to either side we get,<BR>\n" );
document.write( "   sqrt (x+6) - 4 + 4 = x + 4<BR>\n" );
document.write( "==> sqrt(x + 6) = x + 4<BR>\n" );
document.write( "Squaring both the sides we have,<BR>\n" );
document.write( "  x + 6 = (x + 4)^2<BR>\n" );
document.write( "==> x + 6 = x^2 + 8x + 16  [(a+b)^2 = a^2 + 2ab + b^2]<BR>\n" );
document.write( "==> x = x^2 + 8x + 16 - 6<BR>\n" );
document.write( "==> x = x^2 + 8x + 10<BR>\n" );
document.write( "==> 0 = x^2 + 8x + 10 - x [adding -x to both the sides]<BR>\n" );
document.write( "==> 0 = x^2 + 7x + 10<BR>\n" );
document.write( "==> 0 = x^2 + 5x + 2x + 10 [Splitting the middle term]<BR>\n" );
document.write( "==> 0 = x(x+5) + 2(x+5) [Taking out the common factor]<BR>\n" );
document.write( "==> 0 = (x+5)(x+2)<BR>\n" );
document.write( "==> x + 5 = 0   or x+2 = 0<BR>\n" );
document.write( "==> x = -5  or x = -2\r<BR>\n" );
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document.write( "(b)  (5)sqrt(3x+1)=(5)sqrt(x^2-2x-5) <BR>\n" );
document.write( "Dividing both the sides by 5 we get,<BR>\n" );
document.write( "  sqrt(3x+1)= sqrt(x^2-2x-5)<BR>\n" );
document.write( "Squaring both the sides,<BR>\n" );
document.write( "3x + 1  = x^2 - 2x - 5<BR>\n" );
document.write( "==> 3x + 1 - 3x = x^2 - 2x - 5 - 3x [ adding - 3x to both the sides]<BR>\n" );
document.write( "==> 1 = x^2 - 5x - 5 <BR>\n" );
document.write( "==> 0 = x^2 - 5x - 5 - 1 [adding -1 to both the sides]<BR>\n" );
document.write( "==> 0 = x^2 - 5x - 6<BR>\n" );
document.write( "==> 0 = x^2 - 6x + x - 6<BR>\n" );
document.write( "==> 0 = x(x-6) + 1(x-6)<BR>\n" );
document.write( "==> 0 = (x-6)(x+1)<BR>\n" );
document.write( "==> x - 6 = 0   or  x + 1 = 0<BR>\n" );
document.write( "==> x = 6 or x = -1\r<BR>\n" );
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document.write( "(c)[(x+6)^2]/5  + 2 = 3<BR>\n" );
document.write( "==> (x+6)^2 /5 = 3-2 [Adding -2 to both the sides]<BR>\n" );
document.write( "==> (x+6)^2/5 = 1<BR>\n" );
document.write( "Multiplying both the sides by 5 we have,<BR>\n" );
document.write( "(x+6)^2 = 1*5<BR>\n" );
document.write( "==> (x+6)^2 = 5<BR>\n" );
document.write( "==> x^2 + 12x + 36 = 5<BR>\n" );
document.write( "==> x^2 + 12x + 36 - 5 = 0 [add -5 to both the sides]<BR>\n" );
document.write( "==> x^2 + 12x + 31 = 0<BR>\n" );
document.write( "This equation does not have exact values for x.<BR>\n" );
document.write( "Please check the equation.\r<BR>\n" );
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document.write( "Good Luck!!!<BR>\n" );
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