3x(x+3)=2+3x

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Solution for 3x(x+3)=2+3x equation:


Simplifying
3x(x + 3) = 2 + 3x

Reorder the terms:
3x(3 + x) = 2 + 3x
(3 * 3x + x * 3x) = 2 + 3x
(9x + 3x2) = 2 + 3x

Solving
9x + 3x2 = 2 + 3x

Solving for variable 'x'.

Reorder the terms:
-2 + 9x + -3x + 3x2 = 2 + 3x + -2 + -3x

Combine like terms: 9x + -3x = 6x
-2 + 6x + 3x2 = 2 + 3x + -2 + -3x

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

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

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

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

Divide each side by '3'.
-0.6666666667 + 2x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 2x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 2x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + 0.6666666667
2x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
2x + x2 = 0.6666666667

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.6666666667 + 1

Reorder the terms:
1 + 2x + x2 = 0.6666666667 + 1

Combine like terms: 0.6666666667 + 1 = 1.6666666667
1 + 2x + x2 = 1.6666666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.6666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(x + 1) equal to 1.290994449 and -1.290994449.

Subproblem 1

x + 1 = 1.290994449 Simplifying x + 1 = 1.290994449 Reorder the terms: 1 + x = 1.290994449 Solving 1 + x = 1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.290994449 + -1 x = 1.290994449 + -1 Combine like terms: 1.290994449 + -1 = 0.290994449 x = 0.290994449 Simplifying x = 0.290994449

Subproblem 2

x + 1 = -1.290994449 Simplifying x + 1 = -1.290994449 Reorder the terms: 1 + x = -1.290994449 Solving 1 + x = -1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.290994449 + -1 x = -1.290994449 + -1 Combine like terms: -1.290994449 + -1 = -2.290994449 x = -2.290994449 Simplifying x = -2.290994449

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.290994449, -2.290994449}

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