(2x+6)+(-3x^2-4x+6)=

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Solution for (2x+6)+(-3x^2-4x+6)= equation:


Simplifying
(2x + 6) + (-3x2 + -4x + 6) = 0

Reorder the terms:
(6 + 2x) + (-3x2 + -4x + 6) = 0

Remove parenthesis around (6 + 2x)
6 + 2x + (-3x2 + -4x + 6) = 0

Reorder the terms:
6 + 2x + (6 + -4x + -3x2) = 0

Remove parenthesis around (6 + -4x + -3x2)
6 + 2x + 6 + -4x + -3x2 = 0

Reorder the terms:
6 + 6 + 2x + -4x + -3x2 = 0

Combine like terms: 6 + 6 = 12
12 + 2x + -4x + -3x2 = 0

Combine like terms: 2x + -4x = -2x
12 + -2x + -3x2 = 0

Solving
12 + -2x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-4 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.6666666667x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.6666666667x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.6666666667x + x2 = 0 + 4
0.6666666667x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.6666666667x + x2 = 4

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 4 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 4 + 0.1111111112

Combine like terms: 4 + 0.1111111112 = 4.1111111112
0.1111111112 + 0.6666666667x + x2 = 4.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 4.1111111112

Calculate the square root of the right side: 2.02758751

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 2.02758751 and -2.02758751.

Subproblem 1

x + 0.3333333334 = 2.02758751 Simplifying x + 0.3333333334 = 2.02758751 Reorder the terms: 0.3333333334 + x = 2.02758751 Solving 0.3333333334 + x = 2.02758751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 2.02758751 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 2.02758751 + -0.3333333334 x = 2.02758751 + -0.3333333334 Combine like terms: 2.02758751 + -0.3333333334 = 1.6942541766 x = 1.6942541766 Simplifying x = 1.6942541766

Subproblem 2

x + 0.3333333334 = -2.02758751 Simplifying x + 0.3333333334 = -2.02758751 Reorder the terms: 0.3333333334 + x = -2.02758751 Solving 0.3333333334 + x = -2.02758751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -2.02758751 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -2.02758751 + -0.3333333334 x = -2.02758751 + -0.3333333334 Combine like terms: -2.02758751 + -0.3333333334 = -2.3609208434 x = -2.3609208434 Simplifying x = -2.3609208434

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.6942541766, -2.3609208434}

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