(2.8x^2-1.5x+3.4)+(2.7x^2+0.5x-5.7)=

Solution for (2.8x^2-1.5x+3.4)+(2.7x^2+0.5x-5.7)= equation:

Simplifying
(2.8x2 + -1.5x + 3.4) + (2.7x2 + 0.5x + -5.7) = 0

Reorder the terms:
(3.4 + -1.5x + 2.8x2) + (2.7x2 + 0.5x + -5.7) = 0

Remove parenthesis around (3.4 + -1.5x + 2.8x2)
3.4 + -1.5x + 2.8x2 + (2.7x2 + 0.5x + -5.7) = 0

Reorder the terms:
3.4 + -1.5x + 2.8x2 + (-5.7 + 0.5x + 2.7x2) = 0

Remove parenthesis around (-5.7 + 0.5x + 2.7x2)
3.4 + -1.5x + 2.8x2 + -5.7 + 0.5x + 2.7x2 = 0

Reorder the terms:
3.4 + -5.7 + -1.5x + 0.5x + 2.8x2 + 2.7x2 = 0

Combine like terms: 3.4 + -5.7 = -2.3
-2.3 + -1.5x + 0.5x + 2.8x2 + 2.7x2 = 0

Combine like terms: -1.5x + 0.5x = -1x
-2.3 + -1x + 2.8x2 + 2.7x2 = 0

Combine like terms: 2.8x2 + 2.7x2 = 5.5x2
-2.3 + -1x + 5.5x2 = 0

Solving
-2.3 + -1x + 5.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5.5 the coefficient of the squared term: 

Divide each side by '5.5'.
-0.4181818182 + -0.1818181818x + x2 = 0

Move the constant term to the right:

Add '0.4181818182' to each side of the equation.
-0.4181818182 + -0.1818181818x + 0.4181818182 + x2 = 0 + 0.4181818182

Reorder the terms:
-0.4181818182 + 0.4181818182 + -0.1818181818x + x2 = 0 + 0.4181818182

Combine like terms: -0.4181818182 + 0.4181818182 = 0.0000000000
0.0000000000 + -0.1818181818x + x2 = 0 + 0.4181818182
-0.1818181818x + x2 = 0 + 0.4181818182

Combine like terms: 0 + 0.4181818182 = 0.4181818182
-0.1818181818x + x2 = 0.4181818182

The x term is -0.1818181818x.  Take half its coefficient (-0.0909090909).
Square it (0.008264462808) and add it to both sides.

Add '0.008264462808' to each side of the equation.
-0.1818181818x + 0.008264462808 + x2 = 0.4181818182 + 0.008264462808

Reorder the terms:
0.008264462808 + -0.1818181818x + x2 = 0.4181818182 + 0.008264462808

Combine like terms: 0.4181818182 + 0.008264462808 = 0.426446281008
0.008264462808 + -0.1818181818x + x2 = 0.426446281008

Factor a perfect square on the left side:
(x + -0.0909090909)(x + -0.0909090909) = 0.426446281008

Calculate the square root of the right side: 0.653028545

Break this problem into two subproblems by setting 
(x + -0.0909090909) equal to 0.653028545 and -0.653028545.

Subproblem 1
x + -0.0909090909 = 0.653028545

Simplifying
x + -0.0909090909 = 0.653028545

Reorder the terms:
-0.0909090909 + x = 0.653028545

Solving
-0.0909090909 + x = 0.653028545

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.0909090909' to each side of the equation.
-0.0909090909 + 0.0909090909 + x = 0.653028545 + 0.0909090909

Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000
0.0000000000 + x = 0.653028545 + 0.0909090909
x = 0.653028545 + 0.0909090909

Combine like terms: 0.653028545 + 0.0909090909 = 0.7439376359
x = 0.7439376359

Simplifying
x = 0.7439376359

Subproblem 2
x + -0.0909090909 = -0.653028545

Simplifying
x + -0.0909090909 = -0.653028545

Reorder the terms:
-0.0909090909 + x = -0.653028545

Solving
-0.0909090909 + x = -0.653028545

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.0909090909' to each side of the equation.
-0.0909090909 + 0.0909090909 + x = -0.653028545 + 0.0909090909

Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000
0.0000000000 + x = -0.653028545 + 0.0909090909
x = -0.653028545 + 0.0909090909

Combine like terms: -0.653028545 + 0.0909090909 = -0.5621194541
x = -0.5621194541

Simplifying
x = -0.5621194541

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7439376359, -0.5621194541}