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Completing the square Calculator

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1

Solved example of Completing the square

$5\frac{x^2+3x+5}{2x-1}\cdot\frac{2x^2-2x-13}{4x^2-4x+1}$
2

Multiplying the fraction and term

$\frac{2x^2-2x-13}{4x^2-4x+1}\cdot\frac{5\left(x^2+3x+5\right)}{2x-1}$
3

Multiplying fractions

$\frac{5\left(2x^2-2x-13\right)\left(x^2+3x+5\right)}{\left(4x^2-4x+1\right)\left(2x-1\right)}$
4

The trinomial $\left(4x^2-4x+1\right)\left(2x-1\right)$ is perfect square, because it's discriminant is equal to zero

$\Delta=b^2-4ac=-4^2-4\left(4\right)\left(1\right) = 0$
5

Using the perfect square trinomial formula

$a^2+2ab+b^2=(a+b)^2,\:where\:a=\sqrt{4x^2}\:and\:b=\sqrt{1}$
6

Factoring the perfect square trinomial

$\frac{5\left(2x^2-2x-13\right)\left(x^2+3x+5\right)}{\left(2x-1\right)^{2}\left(2x-1\right)}$
7

When multiplying exponents with same base you can add the exponents

$\frac{5\left(2x^2-2x-13\right)\left(x^2+3x+5\right)}{\left(2x-1\right)^{3}}$
8

Factoring by $x$

$\frac{5\left(2x^2-2x-13\right)\left(5+x\left(x+3\right)\right)}{\left(2x-1\right)^{3}}$

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