By the completion or non-completion – This refers to seeing a whole thing even if that whole is not actually there.It is also known as Puranapuranabyham and is used to simplify or solve algebra problems.

**Example 1:**

**x**

^{3}+ 6x^{2}+10x+5 = ?Start by estimating simple quadratic equations that may be similar to the left hand side of this equation. We see that the above is a cubed equation and a simple quadratic will be in the form of (x + *some number*)

^{3 }and also

**(a+b***)*= a^{3}*+ 3a*^{3}^{2}b+3ab^{2}+b^{3}By estimating ,

*estimate #1: (x + 1)*This works out to be x

^{3:}^{3}+ 3x

^{2}+ 3x + 8

*estimate #2: (x + 2)*This works out to x

^{3}^{3}+ 6x

^{2}+ 12x + 8

We'll stop there, because estimate #2 is very close to the equation we're solving.

Subtract from our estimated quadratic equation the left hand side of the problem,

(x

^{3}+ 6x^{2}+ 12x + 8) - (x^{3}+ 6x^{2}+ 11x + 6) = x + 2So, add (x + 2) to both sides of the problem, which leaves us with

**x**^{3}+ 6x^{2}+ 12x + 8 = x + 2We can further simplify this as

**(x + 2)**^{3}= (x + 2).Now we have a common term,

*(x + 2),*on both sides of the equation. Set up another variable, y, to equal (x + 2)y

^{3}= yWe can then infer that y must equal 0 or 1 or -1

If x + 2 = 0 then x = -2

If x + 2 = 1 then x = -1

If x + 2 = -1 then x = -3

Thus,

**x = -1,-2,-3**This sutra can also be used for simplifying or solving quadratic equations and biquadratic equations.

Dear Uma: I love this..Is it similar to pie, IIr2? these natural numbers are magic they go on and on forever...i'd love to learn more! Vedic Math..interesting!

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