# Completing the square Calculator

## Get detailed solutions to your math problems with our Completing the square step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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### Difficult Problems

1

Solved example of Completing the square

$\frac{-x^2-x+2}{-3x^2+14x+5}\geq 0$
2

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($-3$) to all terms

$\frac{-x^2-x+2}{-3\left(x^2-4.6667x-1.6667\right)}\geq 0$
3

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

$\frac{-x^2-x+2}{-3\left(x^2-4.6667x-1.6667+5.4444-5.4444\right)}\geq 0$
4

Factor the perfect square trinomial $x^2+-4.6667x+5.4444$

$\frac{-x^2-x+2}{-3\left(\left(x-2.3333\right)^2-7.1111\right)}\geq 0$
5

Take out the constant $-3$ from the fraction's denominator

$-0.3333\left(\frac{-x^2-x+2}{\left(x-2.3333\right)^2-7.1111}\right)\geq 0$
6

Multiply both sides of the inequality by $-1$, reversing the sign

$0.3333x\leq -0$
7

Divide both sides of the inequation by $0.3333$

$x\leq \frac{-0}{0.3333}$
8

Divide $-0$ by $0.3333$

$x\leq -0$

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