# Completing the square Calculator

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### Difficult Problems

1

Example

${\frac{\left(x+2\right)\left(x+2\right)}{6}}\geq {\frac{x}{3}+\frac{1}{2}}$
2

When multiplying exponents with same base you can add the exponents

$\frac{\left(2+x\right)^2}{6}\geq \frac{1}{2}+\frac{x}{3}$
3

Expanding the polynomial

$\frac{4+4x+x^2}{6}\geq \frac{1}{2}+\frac{x}{3}$
4

Grouping terms

$\frac{4+4x+x^2}{6}-\frac{x}{3}\geq \frac{1}{2}$
5

Multiplying the fraction and term

$\frac{-x}{3}+\frac{4+4x+x^2}{6}\geq \frac{1}{2}$
6

Apply the formula: $\frac{b\cdot a}{c}$$=b\frac{a}{c}$, where $a=-1$, $b=x$ and $c=3$

$\frac{4+4x+x^2}{6}-\frac{1}{3}x\geq \frac{1}{2}$
7

Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$\frac{-4+4+4+4x+x^2}{6}-\frac{1}{3}x\geq \frac{1}{2}$
8

Factor the perfect square trinomial $x^2+4x+4$

$\frac{\left(2+x\right)^2}{6}-\frac{1}{3}x\geq \frac{1}{2}$

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