12x^2-3x-2=0

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


Simplifying
12x2 + -3x + -2 = 0

Reorder the terms:
-2 + -3x + 12x2 = 0

Solving
-2 + -3x + 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'.
-0.1666666667 + -0.25x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -0.25x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -0.25x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -0.25x + x2 = 0 + 0.1666666667
-0.25x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-0.25x + x2 = 0.1666666667

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 0.1666666667 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.1666666667 + 0.015625

Combine like terms: 0.1666666667 + 0.015625 = 0.1822916667
0.015625 + -0.25x + x2 = 0.1822916667

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.1822916667

Calculate the square root of the right side: 0.426956282

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.426956282 and -0.426956282.

Subproblem 1

x + -0.125 = 0.426956282 Simplifying x + -0.125 = 0.426956282 Reorder the terms: -0.125 + x = 0.426956282 Solving -0.125 + x = 0.426956282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.426956282 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.426956282 + 0.125 x = 0.426956282 + 0.125 Combine like terms: 0.426956282 + 0.125 = 0.551956282 x = 0.551956282 Simplifying x = 0.551956282

Subproblem 2

x + -0.125 = -0.426956282 Simplifying x + -0.125 = -0.426956282 Reorder the terms: -0.125 + x = -0.426956282 Solving -0.125 + x = -0.426956282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.426956282 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.426956282 + 0.125 x = -0.426956282 + 0.125 Combine like terms: -0.426956282 + 0.125 = -0.301956282 x = -0.301956282 Simplifying x = -0.301956282

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.551956282, -0.301956282}

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