document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389186>Question 389186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how to Solve the equation x2 + 8x – 2 = 0 using both The quadratic formula and  Completing the square.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275722 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><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=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Quadratic First (~=square root)\r<BR>\n" );
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document.write( "x^(2)+8x-2=0\r<BR>\n" );
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document.write( "Use the quadratic formula to find the solutions.  In this case, the values are a=1, b=8, and c=-2.<BR>\n" );
document.write( "x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0\r<BR>\n" );
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document.write( "Use the standard form of the equation to find a, b, and c for this quadratic.<BR>\n" );
document.write( "a=1, b=8, and c=-2\r<BR>\n" );
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document.write( "Substitute in the values of a=1, b=8, and c=-2.<BR>\n" );
document.write( "x=(-8\~((8)^(2)-4(1)(-2)))/(2(1))\r<BR>\n" );
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document.write( "Simplify the section inside the radical.<BR>\n" );
document.write( "x=(-8\6~(2))/(2(1))\r<BR>\n" );
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document.write( "Simplify the denominator of the quadratic formula.<BR>\n" );
document.write( "x=(-8\6~(2))/(2)\r<BR>\n" );
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document.write( "First, solve the + portion of +-.<BR>\n" );
document.write( "x=(-8+6~(2))/(2)\r<BR>\n" );
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document.write( "Factor out the GCF of 2 from each term in the polynomial.<BR>\n" );
document.write( "x=(2(-4)+2(3~(2)))/(2)\r<BR>\n" );
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document.write( "Factor out the GCF of 2 from -8+6~(2).<BR>\n" );
document.write( "x=(2(-4+3~(2)))/(2)\r<BR>\n" );
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document.write( "Reduce the expression (2(-4+3~(2)))/(2) by removing a factor of 2 from the numerator and denominator.<BR>\n" );
document.write( "x=(-4+3~(2))\r<BR>\n" );
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document.write( "Remove the parentheses around the expression -4+3~(2).<BR>\n" );
document.write( "x=-4+3~(2)\r<BR>\n" );
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document.write( "Next, solve the - portion of +-.<BR>\n" );
document.write( "x=(-8-6~(2))/(2)\r<BR>\n" );
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document.write( "Factor out the GCF of 2 from each term in the polynomial.<BR>\n" );
document.write( "x=(2(-4)+2(-3~(2)))/(2)\r<BR>\n" );
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document.write( "Factor out the GCF of 2 from -8-6~(2).<BR>\n" );
document.write( "x=(2(-4-3~(2)))/(2)\r<BR>\n" );
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document.write( "Reduce the expression (2(-4-3~(2)))/(2) by removing a factor of 2 from the numerator and denominator.<BR>\n" );
document.write( "x=(-4-3~(2))\r<BR>\n" );
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document.write( "Remove the parentheses around the expression -4-3~(2).<BR>\n" );
document.write( "x=-4-3~(2)\r<BR>\n" );
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document.write( "The final answer is the combination of both solutions.<BR>\n" );
document.write( "x=-4+3~(2),-4-3~(2)_x=0.2426407,-8.24264\r<BR>\n" );
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document.write( "Now, completing the square\r<BR>\n" );
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document.write( "x^(2)+8x-2=0\r<BR>\n" );
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document.write( "Since -2 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2 to both sides.<BR>\n" );
document.write( "x^(2)+8x=2\r<BR>\n" );
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document.write( "To create a trinomial square on the left-hand side of the equation, add a value to both sides of the equation that is equal to the square of half the coefficient of x.  In this problem, add (4)^(2) to both sides of the equation.<BR>\n" );
document.write( "x^(2)+8x+16=2+16\r<BR>\n" );
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document.write( "Add 16 to 2 to get 18.<BR>\n" );
document.write( "x^(2)+8x+16=18\r<BR>\n" );
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document.write( "Factor the perfect trinomial square into (x+4)^(2).<BR>\n" );
document.write( "(x+4)^(2)=18\r<BR>\n" );
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document.write( "Take the square root of each side of the equation to setup the solution for x.<BR>\n" );
document.write( "~((x+4)^(2))=\~(18)\r<BR>\n" );
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document.write( "Remove the perfect root factor (x+4) under the radical to solve for x.<BR>\n" );
document.write( "(x+4)=\~(18)\r<BR>\n" );
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document.write( "Pull all perfect square roots out from under the radical.  In this case, remove the 3 because it is a perfect square.<BR>\n" );
document.write( "(x+4)=\3~(2)\r<BR>\n" );
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document.write( "First, substitute in the + portion of the \ to find the first solution.<BR>\n" );
document.write( "(x+4)=3~(2)\r<BR>\n" );
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document.write( "Remove the parentheses around the expression x+4.<BR>\n" );
document.write( "x+4=3~(2)\r<BR>\n" );
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document.write( "Since 4 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4 from both sides.<BR>\n" );
document.write( "x=-4+3~(2)\r<BR>\n" );
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document.write( "Move all terms not containing x to the right-hand side of the equation.<BR>\n" );
document.write( "x=3~(2)-4\r<BR>\n" );
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document.write( "Next, substitute in the - portion of the \ to find the second solution.<BR>\n" );
document.write( "(x+4)=-3~(2)\r<BR>\n" );
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document.write( "Remove the parentheses around the expression x+4.<BR>\n" );
document.write( "x+4=-3~(2)\r<BR>\n" );
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document.write( "Since 4 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4 from both sides.<BR>\n" );
document.write( "x=-4+-3~(2)\r<BR>\n" );
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document.write( "Move all terms not containing x to the right-hand side of the equation.<BR>\n" );
document.write( "x=-3~(2)-4\r<BR>\n" );
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document.write( "The complete solution is the result of both the + and - portions of the solution.<BR>\n" );
document.write( "x=3~(2)-4,-3~(2)-4 </SPAN>\n" );
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