(3.2x^2-7.9x+3.6)+(2.3x^2-6.3x-8.8)=

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Solution for (3.2x^2-7.9x+3.6)+(2.3x^2-6.3x-8.8)= equation:


Simplifying
(3.2x2 + -7.9x + 3.6) + (2.3x2 + -6.3x + -8.8) = 0

Reorder the terms:
(3.6 + -7.9x + 3.2x2) + (2.3x2 + -6.3x + -8.8) = 0

Remove parenthesis around (3.6 + -7.9x + 3.2x2)
3.6 + -7.9x + 3.2x2 + (2.3x2 + -6.3x + -8.8) = 0

Reorder the terms:
3.6 + -7.9x + 3.2x2 + (-8.8 + -6.3x + 2.3x2) = 0

Remove parenthesis around (-8.8 + -6.3x + 2.3x2)
3.6 + -7.9x + 3.2x2 + -8.8 + -6.3x + 2.3x2 = 0

Reorder the terms:
3.6 + -8.8 + -7.9x + -6.3x + 3.2x2 + 2.3x2 = 0

Combine like terms: 3.6 + -8.8 = -5.2
-5.2 + -7.9x + -6.3x + 3.2x2 + 2.3x2 = 0

Combine like terms: -7.9x + -6.3x = -14.2x
-5.2 + -14.2x + 3.2x2 + 2.3x2 = 0

Combine like terms: 3.2x2 + 2.3x2 = 5.5x2
-5.2 + -14.2x + 5.5x2 = 0

Solving
-5.2 + -14.2x + 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'.
-0.9454545455 + -2.581818182x + x2 = 0

Move the constant term to the right:

Add '0.9454545455' to each side of the equation.
-0.9454545455 + -2.581818182x + 0.9454545455 + x2 = 0 + 0.9454545455

Reorder the terms:
-0.9454545455 + 0.9454545455 + -2.581818182x + x2 = 0 + 0.9454545455

Combine like terms: -0.9454545455 + 0.9454545455 = 0.0000000000
0.0000000000 + -2.581818182x + x2 = 0 + 0.9454545455
-2.581818182x + x2 = 0 + 0.9454545455

Combine like terms: 0 + 0.9454545455 = 0.9454545455
-2.581818182x + x2 = 0.9454545455

The x term is -2.581818182x.  Take half its coefficient (-1.290909091).
Square it (1.666446281) and add it to both sides.

Add '1.666446281' to each side of the equation.
-2.581818182x + 1.666446281 + x2 = 0.9454545455 + 1.666446281

Reorder the terms:
1.666446281 + -2.581818182x + x2 = 0.9454545455 + 1.666446281

Combine like terms: 0.9454545455 + 1.666446281 = 2.6119008265
1.666446281 + -2.581818182x + x2 = 2.6119008265

Factor a perfect square on the left side:
(x + -1.290909091)(x + -1.290909091) = 2.6119008265

Calculate the square root of the right side: 1.616137626

Break this problem into two subproblems by setting 
(x + -1.290909091) equal to 1.616137626 and -1.616137626.

Subproblem 1

x + -1.290909091 = 1.616137626 Simplifying x + -1.290909091 = 1.616137626 Reorder the terms: -1.290909091 + x = 1.616137626 Solving -1.290909091 + x = 1.616137626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.290909091' to each side of the equation. -1.290909091 + 1.290909091 + x = 1.616137626 + 1.290909091 Combine like terms: -1.290909091 + 1.290909091 = 0.000000000 0.000000000 + x = 1.616137626 + 1.290909091 x = 1.616137626 + 1.290909091 Combine like terms: 1.616137626 + 1.290909091 = 2.907046717 x = 2.907046717 Simplifying x = 2.907046717

Subproblem 2

x + -1.290909091 = -1.616137626 Simplifying x + -1.290909091 = -1.616137626 Reorder the terms: -1.290909091 + x = -1.616137626 Solving -1.290909091 + x = -1.616137626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.290909091' to each side of the equation. -1.290909091 + 1.290909091 + x = -1.616137626 + 1.290909091 Combine like terms: -1.290909091 + 1.290909091 = 0.000000000 0.000000000 + x = -1.616137626 + 1.290909091 x = -1.616137626 + 1.290909091 Combine like terms: -1.616137626 + 1.290909091 = -0.325228535 x = -0.325228535 Simplifying x = -0.325228535

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.907046717, -0.325228535}

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