The problem asks us to subtract two polynomials: $(2.2x^3 - 5.8x^2 - 2) - (5.3x^3 - 7.1x^2 + 2)$.

1. Problem Description

The problem asks us to subtract two polynomials: $(2.2x^3 - 5.8x^2 - 2) - (5.3x^3 - 7.1x^2 + 2)$.

2. Solution Steps

First, distribute the negative sign to the second polynomial:

$2.2x^3 - 5.8x^2 - 2 - 5.3x^3 + 7.1x^2 - 2$

Next, group like terms:

$(2.2x^3 - 5.3x^3) + (-5.8x^2 + 7.1x^2) + (-2 - 2)$

Combine like terms:

$(2.2 - 5.3)x^3 + (-5.8 + 7.1)x^2 + (-2 - 2)$

$-3.1x^3 + 1.3x^2 - 4$

3. Final Answer

The final answer is $-3.1x^3 + 1.3x^2 - 4$.