-12x^2-4x+3=0

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Solution for -12x^2-4x+3=0 equation:


Simplifying
-12x2 + -4x + 3 = 0

Reorder the terms:
3 + -4x + -12x2 = 0

Solving
3 + -4x + -12x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.25 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.3333333333x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.3333333333x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.3333333333x + x2 = 0 + 0.25
0.3333333333x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.3333333333x + x2 = 0.25

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.25 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.25 + 0.02777777779

Combine like terms: 0.25 + 0.02777777779 = 0.27777777779
0.02777777779 + 0.3333333333x + x2 = 0.27777777779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.27777777779

Calculate the square root of the right side: 0.527046277

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.527046277 and -0.527046277.

Subproblem 1

x + 0.1666666667 = 0.527046277 Simplifying x + 0.1666666667 = 0.527046277 Reorder the terms: 0.1666666667 + x = 0.527046277 Solving 0.1666666667 + x = 0.527046277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.527046277 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.527046277 + -0.1666666667 x = 0.527046277 + -0.1666666667 Combine like terms: 0.527046277 + -0.1666666667 = 0.3603796103 x = 0.3603796103 Simplifying x = 0.3603796103

Subproblem 2

x + 0.1666666667 = -0.527046277 Simplifying x + 0.1666666667 = -0.527046277 Reorder the terms: 0.1666666667 + x = -0.527046277 Solving 0.1666666667 + x = -0.527046277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.527046277 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.527046277 + -0.1666666667 x = -0.527046277 + -0.1666666667 Combine like terms: -0.527046277 + -0.1666666667 = -0.6937129437 x = -0.6937129437 Simplifying x = -0.6937129437

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3603796103, -0.6937129437}

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