12x^2+5x-168=0

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Solution for 12x^2+5x-168=0 equation:


Simplifying
12x2 + 5x + -168 = 0

Reorder the terms:
-168 + 5x + 12x2 = 0

Solving
-168 + 5x + 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'.
-14 + 0.4166666667x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 0.4166666667x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 0.4166666667x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 0.4166666667x + x2 = 0 + 14
0.4166666667x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
0.4166666667x + x2 = 14

The x term is 0.4166666667x.  Take half its coefficient (0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
0.4166666667x + 0.04340277781 + x2 = 14 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667x + x2 = 14 + 0.04340277781

Combine like terms: 14 + 0.04340277781 = 14.04340277781
0.04340277781 + 0.4166666667x + x2 = 14.04340277781

Factor a perfect square on the left side:
(x + 0.2083333334)(x + 0.2083333334) = 14.04340277781

Calculate the square root of the right side: 3.747452839

Break this problem into two subproblems by setting 
(x + 0.2083333334) equal to 3.747452839 and -3.747452839.

Subproblem 1

x + 0.2083333334 = 3.747452839 Simplifying x + 0.2083333334 = 3.747452839 Reorder the terms: 0.2083333334 + x = 3.747452839 Solving 0.2083333334 + x = 3.747452839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 3.747452839 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 3.747452839 + -0.2083333334 x = 3.747452839 + -0.2083333334 Combine like terms: 3.747452839 + -0.2083333334 = 3.5391195056 x = 3.5391195056 Simplifying x = 3.5391195056

Subproblem 2

x + 0.2083333334 = -3.747452839 Simplifying x + 0.2083333334 = -3.747452839 Reorder the terms: 0.2083333334 + x = -3.747452839 Solving 0.2083333334 + x = -3.747452839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -3.747452839 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -3.747452839 + -0.2083333334 x = -3.747452839 + -0.2083333334 Combine like terms: -3.747452839 + -0.2083333334 = -3.9557861724 x = -3.9557861724 Simplifying x = -3.9557861724

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.5391195056, -3.9557861724}

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