3x^2=4x+12

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Solution for 3x^2=4x+12 equation:


Simplifying
3x2 = 4x + 12

Reorder the terms:
3x2 = 12 + 4x

Solving
3x2 = 12 + 4x

Solving for variable 'x'.

Reorder the terms:
-12 + -4x + 3x2 = 12 + 4x + -12 + -4x

Reorder the terms:
-12 + -4x + 3x2 = 12 + -12 + 4x + -4x

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

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

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

Divide each side by '3'.
-4 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1.333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -1.333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1.333333333x + x2 = 0 + 4
-1.333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1.333333333x + x2 = 4

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 4 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 4 + 0.4444444442

Combine like terms: 4 + 0.4444444442 = 4.4444444442
0.4444444442 + -1.333333333x + x2 = 4.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 4.4444444442

Calculate the square root of the right side: 2.108185107

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 2.108185107 and -2.108185107.

Subproblem 1

x + -0.6666666665 = 2.108185107 Simplifying x + -0.6666666665 = 2.108185107 Reorder the terms: -0.6666666665 + x = 2.108185107 Solving -0.6666666665 + x = 2.108185107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.108185107 + 0.6666666665 x = 2.108185107 + 0.6666666665 Combine like terms: 2.108185107 + 0.6666666665 = 2.7748517735 x = 2.7748517735 Simplifying x = 2.7748517735

Subproblem 2

x + -0.6666666665 = -2.108185107 Simplifying x + -0.6666666665 = -2.108185107 Reorder the terms: -0.6666666665 + x = -2.108185107 Solving -0.6666666665 + x = -2.108185107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.108185107 + 0.6666666665 x = -2.108185107 + 0.6666666665 Combine like terms: -2.108185107 + 0.6666666665 = -1.4415184405 x = -1.4415184405 Simplifying x = -1.4415184405

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.7748517735, -1.4415184405}

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