3x^2+2x=464

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Solution for 3x^2+2x=464 equation: 


Simplifying
3x2 + 2x = 464

Reorder the terms:
2x + 3x2 = 464

Solving
2x + 3x2 = 464

Solving for variable 'x'.

Reorder the terms:
-464 + 2x + 3x2 = 464 + -464

Combine like terms: 464 + -464 = 0
-464 + 2x + 3x2 = 0

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

Divide each side by '3'.
-154.6666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '154.6666667' to each side of the equation.
-154.6666667 + 0.6666666667x + 154.6666667 + x2 = 0 + 154.6666667

Reorder the terms:
-154.6666667 + 154.6666667 + 0.6666666667x + x2 = 0 + 154.6666667

Combine like terms: -154.6666667 + 154.6666667 = 0.0000000
0.0000000 + 0.6666666667x + x2 = 0 + 154.6666667
0.6666666667x + x2 = 0 + 154.6666667

Combine like terms: 0 + 154.6666667 = 154.6666667
0.6666666667x + x2 = 154.6666667

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 = 154.6666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 154.6666667 + 0.1111111112

Combine like terms: 154.6666667 + 0.1111111112 = 154.7777778112
0.1111111112 + 0.6666666667x + x2 = 154.7777778112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 154.7777778112

Calculate the square root of the right side: 12.440971739

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 12.440971739 and -12.440971739.


Subproblem 1
x + 0.3333333334 = 12.440971739

Simplifying
x + 0.3333333334 = 12.440971739

Reorder the terms:
0.3333333334 + x = 12.440971739

Solving
0.3333333334 + x = 12.440971739

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 = 12.440971739 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 12.440971739 + -0.3333333334
x = 12.440971739 + -0.3333333334

Combine like terms: 12.440971739 + -0.3333333334 = 12.1076384056
x = 12.1076384056

Simplifying
x = 12.1076384056


Subproblem 2
x + 0.3333333334 = -12.440971739

Simplifying
x + 0.3333333334 = -12.440971739

Reorder the terms:
0.3333333334 + x = -12.440971739

Solving
0.3333333334 + x = -12.440971739

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 = -12.440971739 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -12.440971739 + -0.3333333334
x = -12.440971739 + -0.3333333334

Combine like terms: -12.440971739 + -0.3333333334 = -12.7743050724
x = -12.7743050724

Simplifying
x = -12.7743050724


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.1076384056, -12.7743050724}

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