Question 532498: what is the process and answer to the following quadratic equation using the method from India? x2 -2x -13 =0 Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! There is no India method or American mehod in Algebra.
In 8th. Century BC "Sulbha sutras" gave an account of how Indian Mathemeticians used Geometry to calculate the roots of the quadratic equation.
The constant was shifted to the right side of the equation ax^2+bx +c
ax^2+bx =c
The you then complete the square on the left side by adding a term . Add the same term on the right side.
Take the square root on both sides .
so x will have two values
This is the method which you are referring to.
EXAMPLE
x^2 + 12x -64 =0
x^2 + 12x = 64
4x^2 + 48x = 256
4x^2 + 48x + 144 = 400
(2x+12)^2 = 4x^2 + 48x + 144 = 400
solve for x
2x+12 = 20
2x = 8
x = 4
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2x+12 = -20
2x = -32
x = -16
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---------price ---------------- quantity
Solution I 3 ---------------- x ml
Solution II 55 ------ 130 - x ml
Mixture 39.00% ---------------- 130
3 x + 55 ( 130 - x ) = 39 * 130
3 x + 7150 - 55 x = 5070
3 x - 55 x = 5070 - 7150
-52 x = -2080
/ -52
x = 40 ml 3.00% Solution I
90 ml 55.00% Solution II
x^2-2x-13 can be solved by using the quadratic formula or completing the squares method
Find the roots of the equation by quadratic formula
