12x^2+3x-14=0

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Solution for 12x^2+3x-14=0 equation:


Simplifying
12x2 + 3x + -14 = 0

Reorder the terms:
-14 + 3x + 12x2 = 0

Solving
-14 + 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'.
-1.166666667 + 0.25x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 0.25x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 0.25x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 0.25x + x2 = 0 + 1.166666667
0.25x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
0.25x + x2 = 1.166666667

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 = 1.166666667 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 1.166666667 + 0.015625

Combine like terms: 1.166666667 + 0.015625 = 1.182291667
0.015625 + 0.25x + x2 = 1.182291667

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 1.182291667

Calculate the square root of the right side: 1.087332363

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.087332363 and -1.087332363.

Subproblem 1

x + 0.125 = 1.087332363 Simplifying x + 0.125 = 1.087332363 Reorder the terms: 0.125 + x = 1.087332363 Solving 0.125 + x = 1.087332363 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 = 1.087332363 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.087332363 + -0.125 x = 1.087332363 + -0.125 Combine like terms: 1.087332363 + -0.125 = 0.962332363 x = 0.962332363 Simplifying x = 0.962332363

Subproblem 2

x + 0.125 = -1.087332363 Simplifying x + 0.125 = -1.087332363 Reorder the terms: 0.125 + x = -1.087332363 Solving 0.125 + x = -1.087332363 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 = -1.087332363 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.087332363 + -0.125 x = -1.087332363 + -0.125 Combine like terms: -1.087332363 + -0.125 = -1.212332363 x = -1.212332363 Simplifying x = -1.212332363

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.962332363, -1.212332363}

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