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You can put this solution on YOUR website!
here's a reference that might make some sense out of how to use this method.
\n" ); document.write( "http://answers.yahoo.com/question/index?qid=20100926112059AAcVYbp
\n" ); document.write( "the equation that you need to get the square root of should be a perfect square.
\n" ); document.write( "that's why you can get the square root of it fairly easily (we'll see).
\n" ); document.write( "i'll use that reference as a guide and see if i can solve your problem.
\n" ); document.write( "-----
\n" ); document.write( "x^2 + 12x -64 =0
\n" ); document.write( "a. move the constante term to the right side of the equation:
\n" ); document.write( "x^2 + 12x = 64
\n" ); document.write( "b. multiply each term in the equation for four times the coefficient of the x^2 term:
\n" ); document.write( "4x^2 + 48x = 256
\n" ); document.write( "c. square the coefficient of the original x term and add it to both side of the equation:
\n" ); document.write( "4x^2 + 48x + 144 = 400
\n" ); document.write( "d. Take the square root of both sides
\n" ); document.write( "this is where 4x^2 + 48x + 144 should be a perfect square.
\n" ); document.write( "you should get (ax + b)^2 = 4x^2 + 48x + 144
\n" ); document.write( "we''ll try:
\n" ); document.write( "(2x+12)^2 = 4x^2 + 48x + 144 = 400
\n" ); document.write( "I did the math and confirmed that it is true, so we are left with:
\n" ); document.write( "(2x+12)^2 = 400
\n" ); document.write( "e. Set the left side of the equation to the positive square root on the right side and solve for x
\n" ); document.write( "2x+12 = 20
\n" ); document.write( "2x = 8
\n" ); document.write( "x = 4
\n" ); document.write( "f. Set the left side of the equation equal to the negative square root on the right side and solve for x.
\n" ); document.write( "2x+12 = -20
\n" ); document.write( "2x = -32
\n" ); document.write( "x = -16
\n" ); document.write( "-----
\n" ); document.write( "your answers are:
\n" ); document.write( "x = 4 and x = -16
\n" ); document.write( "the graph of your original equation looks like this:
\n" ); document.write( "
\n" ); document.write( "looks like we have the right answers by looking at the graph.
\n" ); document.write( "-----
\n" ); document.write( "the indian method appears to be an offshoot of the completing the squares method.
\n" ); document.write( "if we solved this equation by the completing the squares method, we would have done the following:
\n" ); document.write( "original equation:
\n" ); document.write( "x^2 + 12x - 64 = 0
\n" ); document.write( "place the constant to the right side of the equation:
\n" ); document.write( "x^2 + 12x = 64
\n" ); document.write( "take 1/2 the coefficient of the x term.
\n" ); document.write( "6
\n" ); document.write( "square it
\n" ); document.write( "36
\n" ); document.write( "add it to the right side of the equation
\n" ); document.write( "x^2 + 12x = 100
\n" ); document.write( "form your squared factor by using 1/2 the coefficient of the x term
\n" ); document.write( "(x+6)^2 = 100
\n" ); document.write( "take the square root of both sides of the equation
\n" ); document.write( "x+6 = +/- 10
\n" ); document.write( "solve for the positive square root of the right side of the equation.
\n" ); document.write( "x = 4
\n" ); document.write( "solve for the negative square root of the right side of the equation.
\n" ); document.write( "x = -16
\n" ); document.write( "you get the same answer.
\n" ); document.write( "with the completing the squares method, the coefficient of the x^2 term has to be equal to 1.
\n" ); document.write( "this is a complicating factor that makes it a little more difficult to solve.
\n" ); document.write( "it appears the indian method does away with that requirement.
\n" ); document.write( "how did they figure out to multiply by 4?
\n" ); document.write( "good question.
\n" ); document.write( "i might look into that when i have time.
\n" ); document.write( "not now though.
\n" ); document.write( "it's enough to finally figure out how to use their method.
\n" ); document.write( "thanks to the reference, i was finally able to.\r
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