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Completing the Square

Tool to make automatic square completion. The square completion is a calculation method allowing to factor a quatradic polynomial expression using polynomial depression.

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Completing the Square -

Tag(s) : Mathematics,Symbolic Computation

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# Completing the Square

## Completing the square solver

Tool to make automatic square completion. The square completion is a calculation method allowing to factor a quatradic polynomial expression using polynomial depression.

### How to complete the square?

dCode can complete the square by depressing a polynomial expression

Let P be $$x^2 +bx + c = 0$$ one adds $$(b/2)^2 - c - (b/2)^2 + c$$ that allows to factor P in $$(x +(b/2))^2 - (b/2)^2 + c$$

dCode can generalize the approach to degrees n superior to 2 by removing the term of degree n-1.

Here is a practical example for a completion by hand: $$p(x) = 2x ^ 2 + 12x + 14$$

Factorize the coefficient $$x ^ 2$$ $$p(x) = 2 (x ^ 2 + 6x + 7)$$ and continue with $$x ^ 2 + 6x + 7$$

Identify the coefficient of $$x$$ here 6 and divide it by 2 to get $$β = 6/2 = 3$$

Use $$β$$ to write $$x ^ 2 + 6x + 7 = (x + 3) ^ 2-β ^ 2 + 7 = (x + 3) ^ 2-2$$

Multiply everything by the coefficient found previously (2) to obtain the completed square: $$p(x) = 2x ^ 2 + 12x + 14 = 2 ((x + 3) ^ 2-2) = 2 (x + 3 ) ^ 2-6$$