3x^2+2x=240

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Solution for 3x^2+2x=240 equation:


Simplifying
3x2 + 2x = 240

Reorder the terms:
2x + 3x2 = 240

Solving
2x + 3x2 = 240

Solving for variable 'x'.

Reorder the terms:
-240 + 2x + 3x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-240 + 2x + 3x2 = 0

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

Divide each side by '3'.
-80 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 0.6666666667x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + 0.6666666667x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 0.6666666667x + x2 = 0 + 80
0.6666666667x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
0.6666666667x + x2 = 80

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 = 80 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 80 + 0.1111111112

Combine like terms: 80 + 0.1111111112 = 80.1111111112
0.1111111112 + 0.6666666667x + x2 = 80.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 80.1111111112

Calculate the square root of the right side: 8.950481055

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 8.950481055 and -8.950481055.

Subproblem 1

x + 0.3333333334 = 8.950481055 Simplifying x + 0.3333333334 = 8.950481055 Reorder the terms: 0.3333333334 + x = 8.950481055 Solving 0.3333333334 + x = 8.950481055 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 = 8.950481055 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 8.950481055 + -0.3333333334 x = 8.950481055 + -0.3333333334 Combine like terms: 8.950481055 + -0.3333333334 = 8.6171477216 x = 8.6171477216 Simplifying x = 8.6171477216

Subproblem 2

x + 0.3333333334 = -8.950481055 Simplifying x + 0.3333333334 = -8.950481055 Reorder the terms: 0.3333333334 + x = -8.950481055 Solving 0.3333333334 + x = -8.950481055 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 = -8.950481055 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -8.950481055 + -0.3333333334 x = -8.950481055 + -0.3333333334 Combine like terms: -8.950481055 + -0.3333333334 = -9.2838143884 x = -9.2838143884 Simplifying x = -9.2838143884

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.6171477216, -9.2838143884}

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