(3x^2+x-4)+(2x^2+2x-3)=

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Solution for (3x^2+x-4)+(2x^2+2x-3)= equation:


Simplifying
(3x2 + x + -4) + (2x2 + 2x + -3) = 0

Reorder the terms:
(-4 + x + 3x2) + (2x2 + 2x + -3) = 0

Remove parenthesis around (-4 + x + 3x2)
-4 + x + 3x2 + (2x2 + 2x + -3) = 0

Reorder the terms:
-4 + x + 3x2 + (-3 + 2x + 2x2) = 0

Remove parenthesis around (-3 + 2x + 2x2)
-4 + x + 3x2 + -3 + 2x + 2x2 = 0

Reorder the terms:
-4 + -3 + x + 2x + 3x2 + 2x2 = 0

Combine like terms: -4 + -3 = -7
-7 + x + 2x + 3x2 + 2x2 = 0

Combine like terms: x + 2x = 3x
-7 + 3x + 3x2 + 2x2 = 0

Combine like terms: 3x2 + 2x2 = 5x2
-7 + 3x + 5x2 = 0

Solving
-7 + 3x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.4 + 0.6x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 0.6x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 0.6x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 0.6x + x2 = 0 + 1.4
0.6x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
0.6x + x2 = 1.4

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 1.4 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 1.4 + 0.09

Combine like terms: 1.4 + 0.09 = 1.49
0.09 + 0.6x + x2 = 1.49

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 1.49

Calculate the square root of the right side: 1.220655562

Break this problem into two subproblems by setting 
(x + 0.3) equal to 1.220655562 and -1.220655562.

Subproblem 1

x + 0.3 = 1.220655562 Simplifying x + 0.3 = 1.220655562 Reorder the terms: 0.3 + x = 1.220655562 Solving 0.3 + x = 1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.220655562 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.220655562 + -0.3 x = 1.220655562 + -0.3 Combine like terms: 1.220655562 + -0.3 = 0.920655562 x = 0.920655562 Simplifying x = 0.920655562

Subproblem 2

x + 0.3 = -1.220655562 Simplifying x + 0.3 = -1.220655562 Reorder the terms: 0.3 + x = -1.220655562 Solving 0.3 + x = -1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.220655562 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.220655562 + -0.3 x = -1.220655562 + -0.3 Combine like terms: -1.220655562 + -0.3 = -1.520655562 x = -1.520655562 Simplifying x = -1.520655562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.920655562, -1.520655562}

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