# Completing the square Calculator

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

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### Difficult Problems

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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