SOLUTION: x2 + 12x -64 =0 a. move the constante term to the right side of the equation: b. multiply each term in the equation for four times the coefficient of the x2 term: c. square the

Question 476602: x2 + 12x -64 =0
a. move the constante term to the right side of the equation:
b. multiply each term in the equation for four times the coefficient of the x2 term:
c. square the coefficient of the orginal x term and add it to both side of the equation:
d. Take the square root of both sides
e. Set the left side of the equation to the positive square root on the right side and solve for x
f. Set the left side of the equation equal to the negative square root on the right side and solve for x.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's a reference that might make some sense out of how to use this method.
http://answers.yahoo.com/question/index?qid=20100926112059AAcVYbp
the equation that you need to get the square root of should be a perfect square.
that's why you can get the square root of it fairly easily (we'll see).
i'll use that reference as a guide and see if i can solve your problem.
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x^2 + 12x -64 =0
a. move the constante term to the right side of the equation:
x^2 + 12x = 64
b. multiply each term in the equation for four times the coefficient of the x^2 term:
4x^2 + 48x = 256
c. square the coefficient of the original x term and add it to both side of the equation:
4x^2 + 48x + 144 = 400
d. Take the square root of both sides
this is where 4x^2 + 48x + 144 should be a perfect square.
you should get (ax + b)^2 = 4x^2 + 48x + 144
we''ll try:
(2x+12)^2 = 4x^2 + 48x + 144 = 400
I did the math and confirmed that it is true, so we are left with:
(2x+12)^2 = 400
e. Set the left side of the equation to the positive square root on the right side and solve for x
2x+12 = 20
2x = 8
x = 4
f. Set the left side of the equation equal to the negative square root on the right side and solve for x.
2x+12 = -20
2x = -32
x = -16
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your answers are:
x = 4 and x = -16
the graph of your original equation looks like this:

looks like we have the right answers by looking at the graph.
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the indian method appears to be an offshoot of the completing the squares method.
if we solved this equation by the completing the squares method, we would have done the following:
original equation:
x^2 + 12x - 64 = 0
place the constant to the right side of the equation:
x^2 + 12x = 64
take 1/2 the coefficient of the x term.
6
square it
36
add it to the right side of the equation
x^2 + 12x = 100
form your squared factor by using 1/2 the coefficient of the x term
(x+6)^2 = 100
take the square root of both sides of the equation
x+6 = +/- 10
solve for the positive square root of the right side of the equation.
x = 4
solve for the negative square root of the right side of the equation.
x = -16
you get the same answer.
with the completing the squares method, the coefficient of the x^2 term has to be equal to 1.
this is a complicating factor that makes it a little more difficult to solve.
it appears the indian method does away with that requirement.
how did they figure out to multiply by 4?
good question.
i might look into that when i have time.
not now though.
it's enough to finally figure out how to use their method.
thanks to the reference, i was finally able to.

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