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

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

Answers to Questions

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 factorizing 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 \( β = 6/2 = 3 \)

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

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